Pierre Picard
email: pierre.picard@polytechnique.edu.

Jennifer Wang
email: jen-wang@nccu.edu.tw.

Kili C Wang

Collusion between Retailers and Customers: The Case of Insurance Fraud in Taiwan

The outsourcing of retail services is frequently at the origin of agency costs, associated with the discretion in the way retailers do their job. This is particularly the case when retailers and customers collude to exploit loopholes in the contracts between producers and customers. In this paper, we analyze how insurance distribution channels may a¤ect such misbehaviors, when car repairers join policyholders to defraud insurers. We focus attention on the Taiwan automobile insurance market by using a database provided by two large Taiwanese automobile insurers. The theoretical underpinning of our analysis is provided by a model of claims fraud with collusion and audit. Our econometric analysis con…rms that fraud occurs through the postponing of claims to the end of the policy year, possibly by …ling a single claim for several events. It highlights the role of car dealer agencies in the collusive fraud mechanism.

Introduction

Vertical relationships frequently involve the outsourcing of services from upstream …rms to downstream retailers. This may be at the origin of agency costs, associated with the discretion in the way retailers do their job. Such agency costs sometimes go through the collusion between retailers and customers, who exploit loopholes in the contracts between producers and customers. Discount fraud and warranty fraud are instances of such customer misbehaviors that involve collusion with retailers or frontline employees.

Discount fraud exploits the special discounts that companies may o¤er under particular circumstances, for instance when discounted products are used for a speci…c purpose, e.g., educational use for softwares. Warranty fraud occurs especially when a service providere.g. a car repairer -replaces a defective part with a new spare part and triggers the producer's warranty, although the defective part was not original and thus was not protected by the warranty. 1 This paper investigates another form of customer misbehavior facilitated by service providers acting on behalf of distributors: insurance fraud. Our empirical focus is on the Taiwan automobile insurance market and on the role of car dealer-owned insurance agents (DOAs) in this market. In such cases, dealers sell not only cars, but also automobile insurance to their clients, and furthermore they own an auto repair shop. Understandably, the multi-faceted activity of dealership agencies and their long-term connection with car owners favor the creation of a mutually advantageous policyholder-DOA alliance. Concerning fraud itself, we will focus attention on the behavior that consists in postponing claims to the last month of the policy year and in merging two losses in a single claim. Deductibles and the bonus-malus mechanism are the underlying reasons for such behavior.

1 See Harris and Daunt (2013) on managerial strategies under the risk of customer misbehavior. Murthy and Djamaludin (2002) survey the literature on new product warranty. Insu¢ cient maintenance e¤ort by buyers and inadequate behavior by retailers are at the origin of a double moral hazard problem in warranty management.

An insurance market model yields the theoretical underpinnings of our analysis. The model focuses on the strategic interaction between, on the one side, policyholders who …le fraudulent claims by colluding with car repairers, and, on the other side, insurers who audit claims. Auditing claims is all the more costly when collusion between policyholders and car repairers is more di¢ cult to detect, which is particularly the case when car repairers are sheltered by DOAs. In addition, should irregularities be detected by the insurer, the high bargaining power of DOAs may allow them to deter insurers from enforcing penalties. The outcome is a higher fraud rate when insurance is distributed by DOAs than through other channels. This is reinforced in the case of deductible contracts, because deductibles increase the gain that policyholders obtain from fraud, and weaken the insurers'incentives to monitor claims.

Our empirical analysis builds on a database obtained from two large insurance companies in Taiwan. This data includes all of the policyholders who have …led an automobile claim in 2010, amounting to nearly 10,000 …les. Our results sustain the prediction that fraud is greater when insurance policies have been sold through DOAs than through other distribution channels, and also that deductibles stimulate fraud. 2 We also show that the causal mechanisms at the origin of fraud (i.e., postponing claims, and possibly …ling one claim for several accidents) are linked to the bonus-malus system in force in Taiwan, and with incentives that are inherent in the design of deductible contracts. This will go through an approach which consists of providing indirect evidence of such misbehaviors and of its mechanisms. 3 More explicitly, we show that the intertemporal pattern of claims 2 Other authors have emphasized the e¤ect of deductibles on insurance fraud. Using data from Québec, Dionne and Gagné (2001) show that the amount of the deductible is a signi…cant determinant of the reported loss when no other vehicle is involved in the accident which led to the claim, and thus when the presence of witnesses is less likely. Miyazaki (2009) highlights through an experimental study that higher deductibles result in a weaker perception that claim padding is an unethical behavior, and thus in a larger propensity toward fraud.

3 Although Dionne et al. (2009a) is an exception, it is usually very di¢ cult to use direct information on fraudulent claims to analyze insurance fraud, either because identi…ed fraud is just the top of the iceberg, or because of insurers'reluctance to share con…dential information on any fraud they are victims of. The preferred approach consists in establishing indirect evidence of fraud. For instance, Dionne and is consistent with policyholder's fraudulent behavior favored by DOAs, after controlling for other explanations, including adverse selection, moral hazard and the money recouping behavior highlighted by Li et al. (2013).

The paper is organized as follows. Section 2 provides further motivation for our analysis. We introduce some factual observations that should convince the reader that there is a signi…cant degree of claim manipulation in the Taiwanese car insurance market, and we describe regular fraud patterns. Section 3 develops a simple theoretical model of insurance fraud that shows how these insurance fraud patterns are linked to speci…c features of insurance contracts, particularly per-claim deductibles, and how the intensity of fraud may be correlated with the insurance distribution channel. Section 4 describes the data in more detail, presents our econometric approach, and discusses our results about claim manipulation. Particular attention is paid to robustness tests, in order to control for other possible explanations of the observed claim pattern. Section 5 concludes. It is followed by an appendix that contains complementary developments of our empirical analysis.

Factual background

As re ‡ected in our data, DOAs hold a substantial market share in the Taiwan automobile insurance market. Our database, presented more extensively in Section 4, includes information yielded by two large Taiwanese insurance companies, refered to as companies 1 and 2, about their 121,952 automobile policyholders and their claims in 2010. In our sample, company 1 sold 44.17% of its automobile policies through DOAs, contrary to company 2 which did not use this distribution channel. In addition to their large market share, DOAs have the bene…t of owning the list of their customers, which increases their bargaining power when they negotiate contractual deals with insurance companies Gagné (2002) and Dionne and Wang (2013) deduce the existence of fraud in automobile theft insurance from the time pattern of claims among the twelve policy months. Pao et al. (2014) provide evidence of opportunistic theft insurance fraud by analysing the claim pattern in areas hit by a typhoon.

or when insurers monitor the claims …led by their clients. In particular, an insurer who discovers a claim manipulation by a DOA may be reluctant to take retaliatory actions because of this strategic advantage of DOAs, who could switch to another insurer. 4 Finally, DOAs work in partnership with car repairers, both being sheltered by car dealers, which provides them with an informational advantage: establishing that a claim has been falsi…ed is particularly di¢ cult and costly when it has been …led through a DOA.

Our study is also related to the speci…c forms of automobile insurance fraud in Taiwan. Li et al. (2013) have observed that a large proportion of automobile insurance claims are …led during the last months of the policy year. This is con…rmed by our own database.

Figure 1 presents the distribution of claims and their average cost (in hundred US dollars) over the twelve policy months. The heavy concentration of claims in the last months of the policy year is striking. Policy years and calendar years do not coincide and, as shown in Figures 2 and3, the concentration of claims during the last months of the policy year is compatible with seasonal ‡uctuations in the number of claims over the calendar year, with peaks during vacation months (June, July and October). In addition, the average claim amount reported in Figure 1 slightly decreases in the …nal policy months. Li et al. (2013) interpret this phenomena as a "premium recouping e¤ect": some policyholders without an accident during the previous months would tend to …le small false claims during the last month of the policy year to express their feeling that they have been unfairly treated by the insurance company.

(Insert Figures 1,2 and 3 here) Some information about insurance contracts is useful for what follows. There are three di¤erent types of automobile physical damage insurance contracts in Taiwan: types A, B and C. Type A and B contracts cover all kinds of collision and non-collision losses, with more exclusions for B than for A,5 while type-C contracts only cover the damages incurred in a collision involving two or more vehicles. Contracts also di¤er in terms of indemnity: Type A contracts o¤er low coverage with a deductible, type B contracts may be purchased with or without a deductible, and type C contracts provide full coverage without a deductible. Claims are per accident, with a speci…c deductible for each claim.

The change in premium is ruled by a bonus-malus system when policyholders renew their contracts with the same insurance company, with a no-claim discount and an increase in premium proportional to the number of claims, without reference to their severity. The policyholders who switch to another insurance company bargain with this company about the new starting point of their bonus-malus record In this setting, opportunist policyholders may take advantage of manipulating claims for several reasons. According to the premium recouping interpretation of Li et al. (2013), defrauders are more likely to be among the policyholders who do not plan to keep a long term relationship with the same insurance company if, on average, such policyholders feel a lower moral cost of defrauding. 6 In our empirical analysis, this will lead us to de…ne a "recoup group" RG that includes the policyholders who have not renewed their contract more than one year after the policy year under consideration. 7 The bonus-malus system and the per-claim deductibles also provide incentives to de-fraud by manipulating the timing of their claims, and possibly by aggregating two events in one single claim. Firstly, the claims …led during the last month of policy year t are not registered in the bonus-malus record of year t + 1 (they will be taken into account in the premium paid in year t + 2), and consequently, the policyholders who plan to renew their contract with the same insurer may be incited to postpone their claim to the last policy month, in order to delay the increase in premium. 8 Secondly, since the bonus-malus record depends on the number of claims and not on their severity, policyholders may be prompted to …le one single claim for two accidents, should a second accident occur. This is even more pro…table in the case of deductible contracts, since deductibles are per-claim: the strategy that consists in postponing the …rst claim and merging any other accident with the …rst one within a single claim yields full coverage for the part of the year that follows the …rst accident.9

Type A and B contracts are subject to such claim manipulation, because they include coverage for losses other than those associated with the collision between two cars. There is no third-party involved in such claims and no police report. On the other hand, the claims …led for type C contracts correspond only to collisions, and they have to include a police report, which makes manipulation very unlikely. In our empirical analysis, the set of policyholders who renew type A or B contracts in 2011, but not in 2012, with the same insurer will be called the "suspicious group" SG because of this incentive to manipulate the bonus-malus system, with subgroups SG1 and SG2 for no-deductible and deductible contracts, respectively.

If we conjecture that a substantial number of claims …led in the last policy month correspond in fact to postponed claims with the cumulated losses of two events, then we should expect that the ratio of "the average cost of …rst claims" over "the average cost of all claims" (hereafter called the …rst claim cost ratio) should increase during this month.

Note however that this prediction could also be interpreted as the outcome of a moral hazard mechanism: this would be the case if a …rst accident made drivers more cautious, and thus they have less severe accidents should a second accident occur during the same policy year. To disentangle these two explanations, we may consider type C contracts as a benchmark to isolate the moral hazard e¤ect, since claims manipulation is unlikely for such contracts. Figure 4 con…rms our intuition: the …rst claim cost ratios for SG1 and SG2 signi…cantly jump in the last month, and this is not the case for type C policies.

(Insert Figure 4 here) At this stage, we may come back to the part played by DOAs. Figure 5 con…rms our intuition that DOAs may favor the manipulation of claims. While the claims …led by the policyholders of the two suspicious groups, SG1 and SG2, are signi…cantly concentrated in the last policy month, this pattern is even more obvious for the policyholders of each subgroup that have purchased insurance from DOAs in company 1. Figure 5 also shows that the last policy month pattern is much less obvious in the benchmark group, which includes those policyholders who are covered by no-deductible contracts and who have not renewed their contract with the same insurance company at the end of the policy year.

(Insert Figure 5 here)

The model

Before further empirical analysis, let us focus attention on the logical links between insurance fraud and relevant features of insurance contracts, particularly the size of deductibles and the distribution channel. This may be done by modelling the strategic interaction between, on the one side, policyholders who defraud by colluding with car repairers, and, on the other, insurers who allocate resources to monitor claims. 10 Consider a population of risk-averse drivers, whose type is de…ned by the couple (i; h) with i 2 fD; Ag and h 2 f1; 2g. Index i refers to the individuals' preference for a speci…c distribution channel through which they purchase insurance: DOA when i = D or standard insurance agents when i = A.11 Index h re ‡ects the individual's degree of absolute risk aversion: h = 1 corresponds to a higher absolute risk aversion than h = 2.

Assume that drivers may have either 0,1 or 2 accidents during the same policy year, with probability 1 and 2 for 1 and 2 accidents, respectively, and 1 + 2 < 1, and also that these probabilities are independent of the policyholders'type. Insurance contracts include a deductible per accident. We respectively denote d ih and P ih the deductible and the premium of the contract chosen by type h individuals who purchase insurance through channel i. Less risk averse individuals choose a larger deductible, and thus we have d i2 > d i1 0. 12 Each accident may be severe or minor, and the corresponding claims small or large, with probability q s or q m = 1 q s , respectively, irrespective of the policyholder's type, and whether it is the …rst or second accident during the policy year. To simplify our analysis of claim manipulation, its is assumed that a large claim exactly doubles a small claim, with loss `and 2`, respectively. Fraud is committed by policyholders who postpone small claims till their last policy month. They will …le one single large claim for two minor accidents presented as a severe accident that occured during the last policy month, should another minor accident occur later during the same policy year. Otherwise, the claim corresponding to the …rst minor accident will be denied because …led outside the permitted time. Fraud reduces the retained cost of the accidents by half since the deductible is paid only once. It also provides a supplementary gain through the manipulation of the bonusmalus system if the policyholder intents to stay with the same insurer at least during the next year.

Defrauding requires collusion with a car repairer, and, in the case of successful fraud, the policyholder and the repairer will share these bene…ts according to their respective bargaining powers. The audit of claims by the insurer makes fraud risky since each member of a policyholder-repairer coalition that is spotted defrauding has to pay a penalty (considered, for simplicity, as a …ne to the government), and, in that case, the claim is fully denied (i.e. the policyholder does not receive an indemnity).

Let us denote by ih and ih the fraud and audit mixed strategy of the policyholder and the insurer, respectively, for a population of type (i; h) individuals. ih is the probability that a type (i; h) policyholder postpones a …rst small claim (when the corresponding minor accident occurs before the last policy month), with the intention to …le a single large claim for two accidents during the last policy month, should another minor accident occur before the end of the year. Fraud is concentrated among those policyholders who are willing to stay with the same insurer at the end of the policy year because they are the ones who bene…t the most through the bonus-malus mechanism. 13 ih is the probability that a large claim (…led by a type (i; h) policyholder) is audited by the insurer. 14 Such large claims correspond either to true severe accidents or to two minor accidents that have been fraudulently aggregated and postponed to the last month). We assume that audit allows the insurer to detect with certainty whether the claim has been manipulated or not.

The expected cost of claims per type (i; h) policyholder is written as

C ih = L D ih + F C ih + AC ih ; ( 1
)
where L is the expected costs of accidents, D ih is the cost retained by the policyholder (in the absence of fraud), F C ih is the cost of fraudulent claims and AC ih is the audit cost.

L and D ih are equal to the expected number of accidents per policyholder 1 + 2 2 multiplied by the weighted average loss per accident and by the deductible per accident, respectively. This gives

L = ( 1 + 2 2 )[q s `+ 2q m `] = ( 1 + 2 2 )(2 q s )`;
and

D ih = ( 1 + 2 2 )d ih :
F C ih is proportional to ih but, for given ih , it decreases linearly with ih , because auditing a larger fraction of large claims reduces average indemnity payment through the detection of falsi…ed claims. DOAs have some bargaining power with insurers and they may intercede with the insurer when a claim is denied for fraud. This intervention holder's type. Note also, that the policy year and the calendar year do not coincide. The beginning of the policy year is evenly distributed over the calendar year among the policyholders. Only the …rst claims that correspond to (true or falsi…ed) severe accidents are audited. For practical reasons, it is assumed that insurers audit all these claims with the same probability, whether they are …led within or outside the last month of the policy year.

is successful with some probability, and thus it decreases the …nancial bene…t drawn by the insurer from spotting a defrauding policyholder-car repairer coalition. Thus, we may write

F C ih = ih [a 1 (d ih ) a 2 (d ih ; i ) ih ]; (2)
with a 1 (d ih ); a 2 (d ih ; i ) > 0, where i is a parameter that measures the bargaining power of distribution channel i, with D > A . 15 We have a 0 1 > 0 and a 0 2d < 0 because the larger the deductible, the larger the …nancial impact of claims falsi…cation and the smaller the gain to the insurer when a claim is denied after audit. We also have a 0 2 < 0 because the distribution channel's bargaining power leads to a smaller insurer's expected bene…t when fraud is detected.

DOAs own and control their repair shop. Thus, it is assumed that auditing a claim (i.e., spending resources to discover whether a claim has been falsi…ed or not) is more costly when insurance has been purchased through a DOA than through a standard insurance agent, because the protection of the DOA makes the detection of the policyholder-repairer collusion more di¢ cult. Let c i be the audit cost when the insurance distribution channel is i = D or A, with c D > c A . Since defrauders manipulate claims by …ling one single large claim for two accidents, the number of large claims …led by type (i; h) policyholders is linearly increasing with ih , which allows us to write16

AC ih = c i ih (a 3 + a 4 ih ): (3)
The insurer chooses ih in [0; 1] in order to minimize C ih , which gives

ih 8 > > > > < > > > > : = 0 if ih < (d ih ; i ; c i ); 2 [0; 1] if ih = (d ih ; i ; c i ); = 1 if ih > (d ih ; i ; c i ); (4)
where

(d; ; c) ca 3 a 2 (d; ) ca 4 : (5)
with 0 d > 0; 0 > 0 and 0 c > 0. Let us assume that (d; ; c) < 1 for the relevant values of d; ; c, which means that systematic fraud would trigger the auditing of all the large claims. Depending on the bribe that they have to pay to car repairers for them to collude (which is not explicitly de…ned here) 17 , on the …ne imposed on spotted defrauders, and on their degree of risk aversion, type h policyholders are willing to defraud if the probability of being caught is larger than a threshold h (P ih ; d ih ) 2 (0; 1). Individuals always defraud when the audit probability is zero, and they never defraud if all large claims are audited:

hence the audit probability h (P ih ; d ih ) for which they are indi¤erent between fraud and honesty is between 0 and 1. 18 This audit probability threshold is type dependent (hence the subscript h in the h function) because it is a¤ected by the intrinsic risk aversion of the policyholder, but it also depends on P ih because an increase in premium may a¤ect the policyholder's risk aversion through a wealth e¤ect, 19 and it is increasing with d ih 17 We may, for instance, assume that policyholders make take it or leave it o¤ers to car repairers. The word "bribe" refers to any form of advantage that the car dealer-repairer …rm may obtain from the arrangement with the policyholder, such as the guarantee of a future car purchase. 18 h could be de…ned in a more explicit way by considering the expected utility of a type h individual who has a minor accident before the last policy month, and who has to choose between two strategies: either honestly …ling a small claim without delay, or postponing her claim to the last policy month in order to …le a single large claim if another minor accident occurs. h is the audit probability that makes the policyholder indi¤erent between these two strategies. 19 For instance, under DARA preferences, an increase in the insurance premium makes the policyholder more risk averse, and thus less prone to conclude a risky fraudulent arrangement with a car repairer. In 13 because an increase in the deductible makes fraud more attractive. Thus, we have

ih 8 > > > > < > > > > : = 0 if ih > h (P ih ; d ih ); 2 [0; 1] if ih = h (P ih ; d ih ); = 1 if ih < h (P ih ; d ih ): (6)
A type (i; h) policyholder who has a minor accident before the last policy month and her insurer play a non-cooperative game, with strategies ih and ih respectively. Its Nash equilibrium is easily characterized. If ih = 0, then (4) gives ih = 0, which implies ih = 1 from (6), hence a contradiction. Similarly, if ih = 1, then (4) gives ih = 1, which implies ih = 0 from (6), hence again a contradiction. Thus, ih 2 (0; 1) and ( 4),( 6) give ih = h (P ih ; d ih ) 2 (0; 1) and ih = (d ih ; i ; c i ) 2 (0; 1). Thus, at equilibrium, the audit probability ih = h (P ih ; d ih ) makes the policyholder indi¤erent between fraud and honesty, and the fraud probability ih = (d ih ; i ; c i ) makes the insurer indi¤erent between auditing and not-auditing. This leads us to simple predictions about the e¤ect of the type of contract and distribution channel on insurance fraud. Firstly, using 0 d > 0 shows that higher deductibles go along with more fraud. Since d 2 > d 1 0, we have i2 > i1 : in other words, for a given distribution channel, fraud is more prevalent among type 2 than type 1 individuals.

More simply, if d 1 = 0, we can say in a shortcut that deductibles encourage fraud. We also have c D > c A and D > A , and thus using 0 > 0 and 0 c > 0 yields Dh > Ah .

Put brie ‡y, for a given type of individual, there is more fraud when insurance has been purchased through the DOA agents than through standard insurance agents, because of the ability of DOAs to shelter their car repairers either from full- ‡edged inquiries or from sanctions.

that case, the larger the insurance premium, the lower the audit probability threshold above which fraud is deterred.

4 Data and testing of hypotheses

The data

The data yielded by companies 1 and 2 is recorded at the individual level and provides detailed information about the policyholders, their insurance contracts and the claims they have …led. Available variables are listed in Table 1. Data was collected over the 2010-2012 period, but our analysis will be restricted to 2010, so that we know whether policyholders subsequently renewed their contracts for less or more than one year. 20 We target the owners of private usage small sedans and small trucks with type A, B or C insurance contracts for automobile physical damage. There are 121; 952 policyholders, and 8:10% of them …led at least one claim in the year 2010, which corresponds to 9; 874 observations. This subset de…nes our "research sample" (i.e., the sub-sample of policyholders with claims).

(Insert Tables 1 and2 here)

The mean values of the variables in the two samples are displayed in the …rst two columns of Table 2, with some signi…cant di¤erences. In particular, the research sample includes a larger proportion of female, middle-aged owners, large-sized and new vehicles.

The insureds in the research sample also tend to purchase higher coverage contracts than those in the whole sample. The percentages of type A or B contracts, and particularly those in the suspicious groups SG1 and SG2, are comparatively much higher in the research sample. The share of the RG group is also larger in the research sample than in the whole sample. Furthermore, the claims record measured by the average bonus-malus coe¢ cient is worse in the research sample than in the whole sample. 21 The other three columns in Table 2 separate the research sample into three subgroups, according to the insurance distribution channels (DOA in company 1 and non-DOA in companies 1 and 2), with signi…cant di¤erences in terms of gender, usage, and vehicle size.

There is also a much higher proportion of new vehicles for the DOA channel, which re ‡ects the fact that, most of the time, a DOA sells an insurance contract when the corresponding dealer sells a new car. The percentage of claims …led during the last month of the policy year, measured by the average value of dummy SC, and the share of the RG group are larger in the DOA channel than in the two other channels.

Evidence on claim manipulation

The Taiwan factual background and our theoretical approach invite us to test several hypotheses about insurance fraud through claim manipulation. We …rstly test the hypothesis that the perspective of contract renewal and the choice of a deductible contract are factors that stimulate fraud. We focus on the fraudulent behavior that consists in manipulating the claim date by moving it to the last policy month, called the "suspicious period", possibly by …ling one claim for two events. We de…ne the fraud rate as the number of claims per policyholder …led during the suspicious period, hence the following Hypothesis 1. 22 Hypothesis 1 (H1): The fraud rate is higher in the suspicious group than in the non-suspicious group, and this is particularly the case for individuals covered by deductible contracts.

Testing H1 amounts to identifying whether there is a conditional dependence between belonging to the suspicious group SG (or to one of its subgroups, SG1 and SG2) on the one side, and …ling a claim within the suspicious period (measured by the dummy SC)

on the other side. We do so through the following three Bivariate Probit models, where 22 Of course, this does not mean that all the claims …led in the suspicious period are fraudulent.

(:) is the cumulative normal distribution function, and X is the vector of explanatory variables (with vectors of coe¢ cients SC ; SG ; :::), including the premium amount and all the variables available for pricing and underwriting decisions. In order to control for the recouping e¤ect, a dummy for RG is also included in X. 23 Model 1:

Prob(SC = 1) = (X SC + " i ) (7) Prob(SG = 1) = (X SG + i ) (8)
Model 2:

Prob(SC = 1) = (X SC + " i ) (9) Prob(SG1 = 1) = (X SG1 + i ) (10)
Model 3:

Prob(SC = 1) = (X SC + " i ) (11) Prob(SG2 = 1) = (X SG2 + i ) (12)
A bootstrapping approach is followed for each model by drawing samples 200 times.

The empirical results of these regressions are listed in Table 3, with a special interest in the estimated residual correlation coe¢ cients. H1 should lead to a positive conditional correlation between …ling a suspicious claim and belonging to a suspicious group. More formally, the estimated residual correlation coe¢ cients of these models, b SC;SG ; b SC;SG1 and b SC;SG2 respectively, should be positive and signi…cantly di¤erent from 0, which leads us to test for the null hypothesis H 0 : SC;SG 0; H 0 : SC;SG1 0 and H 0 : SC;SG2 0, in models 1, 2 and 3 respectively.

The three estimated residual correlation coe¢ cients are signi…cantly positive, which allows us to reject the null hypothis in each model, and thus to state that there is a signi…cantly positive conditional correlation between SC and SG; SG1 or SG2, in each model. In words, in accordance with H1, there is a conditional dependence between belonging to the suspicious group and …ling a claim within the suspicious period, whether the individual is covered by a deductible contract or not. 24 (Insert Table 3 here)

If defrauders postpone their claims to the suspicious period and if they may cumulate losses in a single claim, then the suspicious period should be characterized by high values of …rst-claim cost ratios. This is expressed in Hypothesis 2.

Hypothesis 2: The …rst-claim cost ratio is larger in the suspicious period than during the rest of the policy year, particularly for the suspicious group.

Hypothesis 2 is tested through the following regression:

clmamt = c lastmonth + f f irst + f s f irst lastmonth + X X + e; (13)
which is performed among the claims …led by members of the SG group, where clmamt is the value (in US dollars) of the claim. In this regression, lastmonth and f irst are dummies indicating respectively that the claim was …led during the last month of the 24 Table 3 also o¤ers some interesting byproducts that are worth mentioning. Firstly, the policyholders from the RG group tend to …le their …rst claims in the suspicious period, which echoes the conclusions of Li et al. (2013). Secondly, females …le their …rst claim during the suspicious period more frequently than males, but that does not necessarily re ‡ect a gender e¤ect in fraudulent behavior. It is usual in Taiwan to register cars under the name of females (e.g. a wife or mother), even when the primary driver is a male, in order to bene…t from cheaper insurance premiums. Hence, instead of a gender e¤ect, the above mentioned correlation may just re ‡ect the fact that the policyholders who carefully manage their insurance budget may also try to obtain undue advantage from their insurance company. policy year, and that it was the …rst claim of the policyholder during this policy year.

Regression (13) also includes the interaction variable f irst lastmonth. We perform the above test separately for SG1 and SG2. In our sample, this corresponds to 6,974 claims …led by 6,521 policyholders from SG1, and 695 claims …led by 647 policyholders from SG2. Results are reported in Table 4.

(Insert Table 4 here)

The estimated coe¢ cients of the interaction terms are b f s = 111:7 with p value 0.0852 for SG1, and b f s = 549:2 with p value 0.0007 for SG2, which con…rms the validity of Hypothesis 2, with a lower signi…cance level for SG1 than for SG2. 25 For the sake of completeness, we have also run the regression that explains the value of the claims over the whole sample (not only the SG group) by including dummies SG1; SG2; lastmonth; f irst; RG and their double and triple interaction terms in the explanatory variables. Results con…rm the validity of Hypothesis 2 (see sub-section 6.2 in the Appendix).

Our third hypothesis relates the fraud rate to the insurance distribution channel.

Hypothesis 3 (H3):

The fraud rate in the suspicious group is comparatively even larger when insurance has been purchased through the DOA channel than through other distribution channels.

We test H3 by coming back to Bivariate Probit models 1, 2 and 3 with three distinct sub-samples, including the policyholders who purchased insurance from company 1 through the car dealer channel (sub-sample 1) or through the non-dealer channel (subsample 2), and from company 2 (sub-sample 3), respectively. This leads us to estimated residual correlation coe¢ cients b SC;SG ; b SC;SG1 and b SC;SG2 in each subsample.

(Insert Tables 5,6 and 7 here) channel may simply re ‡ect the fact that, on average, the individuals who take out insurance from DOAs have higher risks, rather than fraudulent behaviors. An additional test, reported in Appendix 6.4, shows that this is not the case. 4. It is also worth investigating whether the validity of our conclusions could be affected by the hypothetical presence of (ex ante) moral hazard. Ex ante moral hazard explains why a more comprehensive insurance coverage may make a driver less cautious. This incentive e¤ect is even stronger for policyholders who had no accidents before the suspicious period, because the bonus-malus system forgives the …rst accident. Hence, under the moral hazard hypothesis, the policyholders from the SG1 group (i.e., those with a no-deductible contract) should be less cautious than those from SG2 (the policyholders with a deductible contract), and, according to the moral hazard interpretation, they should have more severe …rst accidents in the last policy month. The comparison of coe¢ cient b f s in regression (13) for SG1 and SG2 leads to the opposite conclusion.

5. We have analyzed the collusion process as a bilateral car repairer-policyholder agreement, that the insurers may prove only through costly audit. In this setting, insurers -as well as honest policyholders -are victims of hidden claim manipulation. Is it conceivable that insurers themselves are part of collusive agreements ? A possible story along this vein would transform claim manipulation into a strategy to build customer loyalty, deliberately encouraged by insurers, particularly through car dealers. Insurers would be guaranteed of insurance renewals, just as car dealers are guaranteed of future car purchases from this arrangement. Data does not con…rm this interpretation. As previously mentioned, DOAs provide less stable clientele to insurers than other insurance agents, 26 which runs contrary to the idea that encouraging DOAs to manipulate claims could be a way to build customer loyalty. We cannot exclude that claim manipulation is part and parcel of DOAs' marketing strategy, under the form of repeated one-shot deals in order to attract new customers, but this would not create a long-lasting customer loyalty. 27

Conclusion

This paper has focused attention on the policyholder-service provider coalition in insurance mechanisms: how it can a¤ect the credibility of claim auditing, how several patterns of fraud may emerge in the car insurance market, and how service providers and policyholders may draw bene…t from such a coalition. The important role of car dealers in Taiwan provides an exceptional opportunity to analyze this interaction between insurer, policyholder and provider.

It is a fact that the economic analysis of insurance fraud is often based on a very abstract picture of claims fraud (…ling a fraudulent claim although no accident has occurred, or exagerating a claim), but in practice understanding insurance fraud often requires a much more speci…c analysis of the claims fraud process. The Taiwan case o¤ers such a possibility, with fraud frequently taking place through the manipulation of the claim's date in order to avoid a penalty from the bonus-malus system and to reduce the burden of a second deductible, should another accident occur.

We hope to have brought convincing evidence that the intertemporal manipulation of claims is actually a signi…cant determinant of insurance fraud in Taiwan. In particular, policyholders with deductible contracts who intend to renew their policies (the suspicious which is coherent with our analysis of claim manipulation. However, this fraction is even larger when when policyholders have taken out their insurance policies through a DOA than through other distribution channels. 27 Insurers may be obliged to tolerate these misbehaviors, under the threat of car dealers who can guide their customers towards other insurers. The theoretical model of section 3 incorporates this dimension through the large bargaining powers of repairers sheltered by car dealers. group) have a larger propensity to defraud than other policyholders, by postponing their claims until the last month of the policy year, and possibly by merging two events into a single claim. Consequently, there is an increase in the average cost of …rst claims …led by the suspicious group in the last month of the policy year. Furthermore, the collusion between policyholders and car repairers sheltered by car dealers is a crucial mechanism that contributes to the development of fraud in the Taiwanese car insurance market.

The size of claim manipulation in the Taiwan insurance market and the role of DOAs are so signi…cant that it is hard to believe that insurers are unaware of them. Informal exchanges with the industry con…rm that this is the case. Of course, there may be di¤erent views of the underlying mechanisms, varying from granting small advantages to policyholders in order to build customer loyalty and closing ones eyes to small false claims -i.e. the end of year "car wash" and the recouping money behavior, respectively -up to organized large scale insurance fraud through claim manipulation and collusion with car repairers. All these components of customers'misbehaviors are likely to coexist. The lack of response of the Taiwan insurers concerned is more striking. Our analysis suggests that it is in fact very di¢ cult to incentivize DOAs through contractual mechanisms so that …ghting fraud would be in their own interest. The main revenue of car dealers comes from the sales of new vehicles and from the activity of their repair shops. Although DOAs are major intermediaries in the Taiwan insurance market, selling insurance is for most car dealers mainly a way to improve their relationships with car buyers, it is not their core business. Reducing the intensity of fraud through the DOA channel would in fact require a structural reorganization that would be very costly to insurers. Integrating car dealers as part and parcel of the …rm (i.e. regrouping the insurance activity and the sale of cars within a common holding company) might completely change the story. It would reduce the bargaining power of DOAs and, presumably, it would also allow insurers to reduce the asymmetry of information with their DOAs by implementing regular cost reviews, instead of triggering costly audits on a case by case basis, and with the insurer in a position of weakness. Other Taiwanese insurers have made that choice. The size of fraud in the Taiwan automobile insurance market should persuade insurers that comparing the costs and bene…ts of these decentralized and integrated schemes is of utmost importance.

Appendix

6.1 Testing Hypothesis 1 and 3 through two-stage regressions Dionne et al. (2001) follow a two-stage approach in order to analyze the link between the claim frequency and the choice of a deductible (vs full insurance) contract. This led them to appraise the conditional dependence between these two variables by the estimated coe¢ cient of the deductible contract dummy in the regression that explains the claim frequency. We have checked the robustness of our conclusions using a similar method.

Stage 1 coincides with the regressions (2), ( 4) and ( 6 or SG 2 is positive and signi…cantly di¤erent from 0 at the 1% signi…cance threshold level for the three de…nitions of the suspicious group, which con…rms the validity of our Hypothesis 1. We have also added the interaction terms D c SG and D SG, and also C 2 c SG and C 2 SG (and the same for SG 1 and SG 2 ), where C 2 is a dummy for company 2 where contracts are not sold through car dealers. In the three models, the coe¢ cients of D SG; D SG 1 and D SG 2 are positive and signi…cantly di¤erent from 0, contrary to the coe¢ cients of C 2 SG; C 2 SG 1 and C 2 SG 2 , which provides additional evidence on the validity of our Hypothesis 3.

Additional test for Hypothesis 2

The regression that explains the claim value (hitherto regression (13)) has also been performed over the whole sample (not only the SG group) by adding dummies SG 1

and SG 2 and their double and triple interaction with lastmonth and f irst, among the explanatory variables. Furthermore, in order to be able to distinguish fraud going through claim manipulation from the premium recouping behavior, the set of explanatory variables also includes RG and its double and triple interaction with lastmonth and f irst. This leads to the following regression: (Insert Table 12 here)

clmamt = S1 SG 1 + S2 SG 2 + RG RG + C lastmonth + f f irst + Rf RG f irst + Cf lastmonth f irst + Sf 1 SG 1 f irst + Sf 2 SG 2 f irst + SC1 SG 1 lastmonth + SC2 SG 2 lastmonth + SC2 SG 2 lastmonth + RC RG lastm + SCf 1 SG 1 lastmonth f irst + SCf 2 SG 2 lastmonth f irst + RCf RG lastmonth f irst + X X + e:
Panel A of Table 12 con…rms that this is the case for the suspicious and non-suspicious groups. Furthermore, the di¤erence of the prediction error is signi…cantly larger in absolute value in the suspicious groups, especially in SG 2 , than in the non-suspicious group.

This con…rms the manipulation of claims, beyond any possible hidden information about policyholders'risk types.

Secondly, we know that adverse selection may lead to a positive correlation between the contract coverage and the probability of …ling claims, but it does not induce any particular timing for claims over the year. Panel B of Table 12 provides the incident rate ratio for SG 1 and SG 2 , as well as in the non-suspicious group. In SG 1 and SG 2 , the incident rate ratios are signi…cantly higher in the last policy month than in the other months, and these last month hazard rates are signi…cantly higher than in the non-suspicious group, which con…rms once again that claim manipulation does occur. The fact that the last month hazard rate is even larger for SG 2 than for SG 1 con…rms that our observations cannot be attributed to adverse selection.

Additional test for Hypothesis 3

It is legitimate to question whether the higher expected cost of claims in the DOA channel may simply re ‡ect the fact that, on average, the individuals who take out insurance from DOAs have higher risks, rather than fraudulent behaviors. This issue may be clari…ed by estimating the claim amount using the following OLS regression:

clmamt = 0 + D D + C2 C 2 + AB AB + DAB D AB + C2AB C2 AB + X X + e;
where AB is a dummy for contracts of type A or B, with type C contracts as counterpart.

The estimated results are in Table 13, with b AB positive and signi…cantly di¤erent from 0, which means type A and B contracts are associated with claim costs that are signi…cantly larger than for type C. b D is negative, but not signi…cantly di¤erent from 0. Furthermore, C2 is positive and signi…cantly di¤erent from 0. We may deduce from these results that the contracts are not associated with higher claim costs when they are sold through the DOA channel rather than through other channels. Meanwhile, the contracts of company 2 have higher claim costs than those of company 1. Furthermore, b DAB is negative and b C2AB is positive, both coe¢ cients being signi…cantly di¤erent from 0. This means that the type A and B contracts going through the car dealer channel in company 1 (respect.

through other distribution channels in company 2) entail comparatively lower claim costs (respect. higher claim costs) than other contracts. In other words, the increase in claim costs is not an intrinsic characteristic of the distribution channel: it re ‡ects the fraudulent behaviors of some policyholders (the suspicious groups) who may take advantage of the manipulation of claims, and this behavior is facilitated by DOAs.

(Insert Table 13 here)

  Performing this regression among the 10,684 claims …led by the members of the research sample gives b SCf 1 = 156:06 with p-value 0:0513, b SCf 2 = 885:23 with p-value 0.0004, and RCf = 200:52 with p-value 0:0233. The inequalities b SCf 2 > b SCf 1 > 0once again validate Hypothesis 2. Symmetrically, RCf = 200:52 < 0 con…rms that members of the RG group tend to …le small claims at the end of the policy year, when they have not …led a claim during the previous months. 286.3 Taking adverse selection into accountIn a setting with adverse selection, past and future claim experiences may be linked, but man-made claim manipulation should reduce the predictive power of this link. To check if this is actually the case, we have used the 2010 data to run two Probit regressions that estimate the probability of …ling a claim either in any month of 2011 or in the suspicious period of 2011, respectively. The regressions were run separately for the suspicious and non-suspicious groups. Observing the policyholders'2011 claim records allows us to calculate the prediction error for the claims …led either throughout 2011 or during the suspicious period of the same year. In a second stage, we may use a t-test to check whether the …rst prediction error is smaller than the second one.

On average, DOAs sell more policies than other agents (three times more on average and considerably more for the largest DOAs), and their market power is particularly signi…cant for deductible contracts. They are independent agents, and, as emphasized byMayers and Smith (1981), this status gives them more discretion in claim administration (e.g. they may intercede on behalf of their customers at the claim settlement stage) because they can credibly threaten to switch their business from one insurer to another. Actually, DOAs provide comparatively less stable customers to insurers than other insurance agents, with continuation rates (i.e. the fraction of customers who continue purchasing insurance from the same insurer year on year) which are about sixty percent for DOAs and seventy to eighty percent for other insurance agents.

Type B contracts cover all the areas of type-A contracts, except the non-collision losses caused by intentional damage, vandalism, and any unidenti…ed reasons.

It is well known that insurance fraud is often associated with the feeling that the insurance company is unfair; see[START_REF] Fukukawa | An eye for an eye : investigating the impact of consumer perception of corporate unfairness on aberrant consumer behavior[END_REF],[START_REF] Miyazaki | Perceived ethicality of insurance claim fraud : do higher deductibles lead to lower ethical standards[END_REF] and[START_REF] Tennyson | Economic institutions and individual ethics : a study of consumer attitudes toward insurance fraud[END_REF][START_REF] Tennyson | Insurance experience and consumers'attitudes toward insurance fraud[END_REF]. The premium recouping phenomenon could re ‡ect a kind of resentment against insurers, particularly from policyholders who have not …led a claim during the policy year.

Because of the bonus-malus system, the policyholders who intend to renew their contract only one year have the same incentive to defraud by manipulating claims as the policyholders who have the intention of switching insurers at the end of the policy year. See below for details.

In addition, the bonus-malus system forgives the …rst accident for drivers who have had no other accidents for three years, which provides an even larger manipulation gain.

Since 1996, the per-claim deductible is increasing with the number of claims, which strengthen even more the incentives to manipulate claims.

The model features the non-cooperative interaction between policyholders and insurers, in a costly state veri…cation setting as in[START_REF] Picard | Auditing claims in insurance market with fraud: the credibility issue[END_REF]. For the sake of brevity, several aspects of the insurance market analysis are deliberately overlooked here. This particularly concerns the way individuals choose their contracts and their insurance distribution channel, depending on their risk aversion and on their intinsic preference for a speci…c channel.

For the sake of simplicity and brevity, we do not analyze the reasons for which an individual may prefer to purchase insurance through a car dealer or through another distribution channel. Such preferences are likely to depend on many factors, such as the valuation of time saved by bundling the purchase of a new car and the taking out of an insurance policy, the repeated relationship between individuals and car dealers that also provide repair services, or the level of trust in car dealers.

For notational simplicity, we assume that the deductible is the same whether it is the …rst or second claim during the policy year.

The policyholders who may bene…t the most from defrauding through claim manipulation are those who have a …rst minor accident before the last month of their policy year and who do not intend to switch insurers. If these policyholders are just indi¤erent between defrauding and not-defrauding, as will be the case at the equilibrium of the policyholder-insurer interaction game presented in the following analysis, then the other policyholders will be detered from defrauding.

Note that the degree of risk aversion is not directly observed by the insurer. However, individuals choose di¤erent contracts (i.e., di¤erent deductibles) depending on their risk aversion, and thus insurers can condition their audit probability on the level of the deductible, and thus indirectly on the policy-

Fraud, as it is described, may be committed by policyholders who intend to renew their insurance policy and who have two accidents, the …rst one being minor and occurring before the last month of the policy year. Thus, a 1 (d ih ) and a 2i (d ih ) depend on the probability that a type (i; h) individual is in this situation, which depends on 1 ; 2 and q s , but also on the timing of accidents throughout the policy year, which is left undescribed for the sake of brevity.

Here also, a 3 and a 4 depend on 1 ; 2 and q s (but not on d ih ), and furthermore a 4 depends on the timing of accidents throughout the policy year.

In what follows, years are policy years: a contract corresponds to year 2010 if it started in 2010.

The bonus-malus coe¢ cient is a multiplier applied to the actuarial premium: the larger this coe¢cient, the larger the premium charged to the policyholder.

The pricing and underwriting variables include all the observable characteristics of the insured (e.g. age, gender, bonus malus coe¢ cient, etc), and the characteristics of the vehicle (e.g. age, brand, registered area, etc). The premium amount and the recoup dummy are also included. In words, X includes all the variables listed in the …rst part of Table1, and logprem and recoup in the second part.

This is consistent with the fact that the policyholders with deductible contracts (i.e. the SG2 subgroup) have a greater incentive to …le a single claim for two events than the policyholders with no-deductible contracts (the SG1 subgroup).

As shown in Table1, the average value of SG, i.e., the fraction of policyholders who have renewed their contract only for one year, is much larger in the sub-sample with claims than in the global sample,

The tables with detailed results are not reported here for the sake of brevity. They are available from the authors upon request.

Detailed results are displayed in Tables 5, 6 and 7, for models 1, 2 and 3 respectively.

The following table summarizes our conclusions about the conditional dependence between SC on the one side, and SG; SG1 and SG2 on the other, with and refering to signi…cance levels at the 10% and 1% thresholds, respectively. (hence with SG1 and SG2 instead of SG). As before, we proceeded by bootstrapping each model 200 times, which allowed us to derive the standard deviation for each residual jected at the 1% signi…cance level, and the same applies if SG is replaced by SG1 or SG2.

In other words, whatever the de…nition of the suspicious group (SG; SG1 or SG2), the conditional correlation between …ling a suspicious claim and belonging to the suspicious group is signi…cantly larger when contracts are sold through the car dealer associated with company 1 than through another distribution channel of company 1 or from company 2.

(Insert Table 8 here)

Robustness tests

1. To check the robustness of our conclusions, we have also tested Hypothesis 1 and Hypothesis 3 by following a two-stage approach inspired from Dionne et al. (2001).

The results are reported and discussed in Appendix 6.1. They con…rm our conclusion about the conditional correlation between SG, SG1 or SG2 and SC. They also con…rm that these conditional correlations are comparatively higher when the contracts are sold by company 1 through the dealer channel than through other channels.

2. In a setting with adverse selection, past and future claim experiences may be linked, but man-made claim manipulation should reduce the predictive power of this link.

Furthermore, adverse selection may lead to a positive correlation between the coverage and the probability of …ling claims, but it does not induce any particular timing for claims. These observations open the door to additional tests reported in Appendix 6.3, con…rming that our conclusions on claim manipulation are not called into question by hidden information on risk types.

3. It is legitimate to question whether the higher expected cost of claims in the DOA


come

Introduction to Text

Mining: from basics to applications Luca Foppiano

About me

• Started as software engineer, currently working in Text and Data mining.

• 7 years at the European Patent Office (NL)

• 3 years at Inria (National Institute for Computer science and Mathematics) (FR)

• Currently at NIMS (National Institute for Material Science) (JP)

• Main topics: Machine Learning and TDM

Text and Data Mining

• Text Mining or TDM (Text and Data Mining) is the process of deriving high quality information from other sources

• Information retrieval • Information extraction (mining)
• Knowledge management

• The approach for TDM require an understanding (shallow or more deep) of the text • NLP (Natural Language Processing) is a very wide subfield, studying ways to program computers to interact with natural language data (text for example)

Ideal conditions

• Scalability • Repeateability • Genericity (*)
• Automatic

Artificial Intelligence

• Artificial Intelligence (shorten for AI) is the branch of Computer Science that study methods and tecniques aiming to mimic the functioning of the human brain

• Origin dating back to the 50' (Alan Turing, Turing test)

• Continuously evolving, more than 50 years of investments

• Most known applications: OCR, Voice Recognition, Self Driving Cars, Spam recognition, etc…

AI Evolution

Deep Learning

The state-of-the-art based on the brain representation concept defined in the 50 by Turing and researched in the 70 with the neural networks.

Computers weren't powerful enough so for deep networks had only 2-3 layers (overtaken by statistical models, like SVM, CRF)

In the last decade with the serveral improvements: -computer power (thanks gamers!!) -algorithms -data availability

The brain model Deep Learning

• There are still grey areas

• The knowledge required to get decent results has decresed -"if in doubt, add a layer"

• Less needs to tune • Google provided a pre-trained models on millions of sentences • Each word can be transformed into a vector

• "Similar" words output similar vectors

• called Embeddings

TDM in action

• Search

• Recommendation systems (Netflix, Amazon…)

• Analytics

• Disambiguation / Entity Linking

• Mining (extraction of specific information)

Search

• Ambiguities in wording

• Correctly infer the context (short query)

• How to prioritise the results? Nobody goes to page 2

• Lot of data, but not clean

•

  Common approach is to use as much data as possible and let the network figure out what to do with it DL and TDM • Images or Audio are easily representable as vectors or matrices… • Text is shallow, require an alternative representation of their basic component: words • How to represent words?Word 2 Vec• First draft published byGoogle in 2013 (word2vec)


Sashikanth Rapeti

Ansuman Babu

Ansuman Babu The Emerging

THE EMERGING NEED FOR A ROBUST GPS NAVIGATION, SURVEILLANCE AND ENVIRONMENTAL MONITORING IN LATIN AMERICA AND SAGANS , THE OVERALL HUB OF TECHNOLOGICAL SOLUTIONS

Keywords: GPS, SAGANS, UNSAAC SAT, PeruSAT-1, CHASQUI 1, Green satellite, UAPSAT-1, Galileo Positioning system, SIT( Satellite Integrated Technology), space and aircraft propulsion

research documents, whether they are published or not. The documents may come

INTRODUCTION

A direct leap into the technical details into SAGANS can be exciting, but will be incomplete without a meager flavor of geographical analysis of the continent in terms of its topography. This geographical analysis will provide the enthusiastic readers of scientific and non-scientific backgrounds the necessary information as to why SAGANS is much required for the continent. Moreover, SAGANS will be acting like a shield to the natural resources of the continent by keeping an "Eagle-eye" surveillance monitoring over entire latin america. SAGANS accommodates many additional features compared to conventional GPS systems, going beyond the phase differential approach, which certainly includes and integrates the space weather effects to the navigation and other diversified technological applications in the continent. SAGANS is not just another advanced technological show-off of any particular nation for political benefits, but a much awaited and promising advanced technological hub of solutions to various problems faced by the people in the continent , be it technological , agricultural, safety and integrity of countries, navigation, mining, natural resources, medical research, monitoring and advanced warning systems concerning the natural calamities etc.

I. A BRIEF GEOGRAPHICAL ANALYSIS

Latin America is a special continent in terms of natural resources, pleasant atmospheric and climatic conditions, with very less land, air and water pollution. Every country in the continent is gifted with ample natural resources and people with crystal clear mindset. It is interesting to note that some countries enjoy the calm and deep blue Pacific waters, while bigger countries relish the jumping and turbulent green waters of the Atlantic. Countries like Bolivia and Paraguay are fully landlocked, but Uruguay enjoys the Atlantic waters, while bordering with Brazil and Argentina. Most of the continent is covered with the most beautiful Amazon rain forests and the exciting Andes mountain ranges along Chile to Peru. Every country has its own vibrant cultural features as well. Although every country has its own set of laws, still intracontinental travel is very exciting in terms of the various UNESCO heritage sites like Machupichu in Peru and the old colonial architecture buildings in Chile, Argentina, Bolivia, Ecuador, Colombia etc. Brazil being the largest country occupying more than 50 % of the land mass of the continent is rich in natural resources with the Amazon rain forests which is home for diversified wildlife and aquatic species found nowhere else on the planet. The Andes leaves a huge vertical footprint on the continent by extending from Venezuela in the north, passing through Colombia, Ecuador, Peru, Bolivia, Argentina and finally Chile. These mountain ranges, running along the western direction of the continent, is certainly among the world's longest mountain ranges. The Andes has a varied terrain encompassing glaciers, volcanoes, grassland, desert, lakes and forests. The Andes mountain ranges shelter the pre-Columbian archaeological sites and wildlife including chinchillas and condors. Obviously, the entire continent itself tops the list of the various tourism destinations of many people in the world. The natural resources connect each country in a harmonious way that is quite obvious. It is worth-noting that Brazil is the only nation that speaks Portuguese language and the other countries mostly speak Spanish. MONITORING, NAVIGATION AND GLOBAL POSITIONING SYSTEM In SOUTH AMERICA Broadly speaking, when every continent has its own GPS ( mostly individual countries like USA, china, Russia etc have their own GPS, with the exception of Europe trying to have a common GPS for entire continent , GALILEO POSITIONING SYSTEM), the need of the hour is to have a common space agency ( integrating all space agencies in the continent) , working towards common goals in the space and aerospace sector, and a common GPS system for the entire Latin American continent, which will have its own varied applications like Environmental monitoring, GPS, land mapping, sea floor mapping and much more. In addition, Space and aerospace technologies are ruling a nation's economy in every aspect in the 21 st century. This is the most common and strong opinion by a large scientific and technological community of South American continent comprising of engineers, scientists, research scholars, professors, and even students. A common space program naturally provides a robust platform for the creation of a common space agency in the continent. This in turn requires a much more robust set of goals regarding the various space satellite missions which actually form the integral core part of the common space program which must cater to the various technological needs of citizens, students, farmers and agriculturists, academicians, educationists, scientists, engineers, militaries, governmental agencies etc in a much effective manner with precision and accuracy.

III. DOES SOUTH AMERICA REALLY IN NEED OF SAGANS and GPS ?

Latin America needs an integrated GPS system absolutely at this crucial juncture, specially when it comes to a nation's and broadly speaking, the entire continent's safety, security and integrity which is undeniable under any circumstances. A positive inter-continental GPS is much ahead of us in the distant future, when space and interplanetary travel becomes a common and affordable reality for the residents of the earth. Since, SAGANS features much additional aspects in addition to navigation, it is more of a desperate prerequisite to have surveillance monitoring of the rich natural resources of the continent.

IV. THE NATURAL DISASTERS AND THE EMERGING NEED FOR ENVIRONMENTAL

MONITORING IN LATIN AMERICA Natural disasters are a frightening nightmare to any country and any continent. The 2010 earthquake of Chile is one such example. If the technology which had been developed is of no use at the crucial moment, then that definitely means we had developed a poor technology and our technology needs to be modified to save the lives of at least fellow humans. Human society is important for all the other living entities and we need to make sure whether we are living with other species and nature in harmony or not. Moreover, Natural disasters is the result of the collective aspects of Newton's third law. Other species like animals, birds etc generally do not go against the laws of nature for which Newton's third law is an integral part. The humans being a little more intelligent than other species had made it a habit to go against the natural laws, specially the newton's third law, only to invite more natural disasters which in fact counter balance the disturbance caused in nature. These natural disasters can be the result of an ecological imbalance caused by humans, as the disasters caused by other species like animals, birds, insects etc is never heard of. The ecological imbalance caused by humans can be like illegal mining, dumping of much chemical waste and toxic substances into rivers, small water bodies etc resulting in water pollution, soil poisoning , increase in toxicity in air, water and land etc. Hence, there is an emergent need to conserve nature in every aspect and space technology can be utilized at its best to fulfill this purpose. Therefore, environmental monitoring is of utmost importance to South America. The world had witnessed in the recent past and is witnessing the severe impact of heavy industrialization, land, air and water pollution in many countries.

V. DIVERSIFIED PURPOSES SERVED BY MEANS OF A ROBUST SPACE SATELLITE AND GPS

TECHNOLOGY Most of the problems in agriculture, water resources, conservation of plants and trees, soil fertility etc are all interlinked with each other for which the satellite technology can offer good solutions in terms of monitoring and processing the data, providing the users with the required information etc. Also, some critical aspects of vehicle navigation, transit systems can be utilized for military purposes to put the miscreants who disturb the peacefulness of the society, under control. On an overall basis, this technology will generate revenue for the government, governmental agencies, universities, users in terms of business, retail industry, agriculture etc. The main motive of SAGANS is a win-win situation to the governments as well as its citizens ( technologists and users as well).

VI. LATIN AMERICA IS IN NEED OF HEALTHY TECHNOLOGICAL SOLUTIONS FOR THE PRESENT AND FUTURE EDUCATION SYSTEMS IN THE CONTINENT ICFES of

Colombia is a governmental body responsible for educational development from the school level to higher education in the country. Like Colombia, many nations in Latin America are interested in nature-friendly technologies that can be taught right from the school level to inculcate students the importance of nature and the proper utilization of natural resources, which bring prosperity and happiness in the human society. Hence, from a satellite based classroom in Ecuador etc, the applications of the SAGANS will play a major role in the futuristic education systems in the continent. When the continent shields the world with its supply of fresh oxygen, the continent can also be like an innovation hub in futuristic nature friendly and technological education systems. When students , with the help of professors can make a satellite orbit and operate in space, then they can also take part in the revolutionary development of sustainable and renewable technologies. They can even make a ' GREEN SATELLITE' orbit in space with utmost efficiency in terms of lifetime and operational stability of the satellite in space.

VII. THE FUNDAMENTAL IDEA OF SAGANS

The fundamental idea of SAGANS stems from the stark reality of the dire necessity of a great beginning of innovative, nature-harmonious technologies and their inclusion in the futuristic education systems in the Latin American continent. When Brazil can implement ethanol in the automobile industry as an alternative to the burning issue of petrol and diesel, then much more can be done in the form of GREEN TECHNOLOGIES, which can also be embedded in technologies like space craft and aircraft propulsion. Moreover, Space and aerospace are two inter-connected, highly effective technologies that are indeed running a country and its economy these days. Misuse of these technologies will result in a society of chaos as is evident in some countries in the world.

VIII. SAGANS -THE NEXT TECHNOLOGICAL FRONTIER OF SOUTH AMERICA IN THE NEAR

FUTURE This is quite obvious because SAGANS is not just a single satellite to be launched by a single country just for its own prestige in the international technological arena, but a combined technological effort for the benefit of a continent at large. SAGANS is a hub of technological solutions that transform the lives of people in the continent in every aspect. But SAGANS should be implemented systematically and must be handled with utmost care. This will definitely lead to a shower of positive results in terms of technology, agriculture, economy boost of the country etc. Indeed, SAGANS will transform the technological arena in the continent , by offering more work for technologists, researchers, students for more than ten years and will also provide technological facilities to users, governments, military etc. The minimum operational stability should be 25 years in case of the satellites in SAGANS. More number of SIT (satellite integrated Technology) classrooms can be expanded in every country in the continent to revolutionize the education system in the entire continent. The Green Satellite idea and the fuel for the green satellites etc can be explored in the consecutive papers for which Super-fluid Helium -3 and helium -4 can be considered as a propellant because of their low temperature existence and the refrigerant characteristic feature. In addition, the electromagnetic propulsion technology can be utilized for the green satellites used for SAGANS. Innovative technologies will play a major role in SAGANS in an indigenous manner.

IX. ROLE PLAYED BY PERU IN THE DEVELOPMENT OF NANO-SATELLITE TECHNOLOGY, MILESTONES ACHIEVED AND HIGHLY RESPONSIBLE ROLE REGARDING SAGANS AWAITING

FOR PERU From the very recent past to the present, Peru has always been playing a highly dynamic and active role(in the continent) in the development of the category of small satellites technically known as Nano satellites and Femto satellites, be it PeruSAT-1 , the high resolution Optical Earth observation satellite, whose success story as per the company AIRBUS is as follows, Regarding the exploration of other planets, the country is very much active in the "SIMULATION OF MARS EXPLORATION". In this regard, Brazil, Argentina, have their own vibrant space satellite missions covering various other aspects of environmental monitoring and surveillance. Chile and Colombia are gradually catching up the pace in the space technologies. Uruguay and Bolivia are gearing up for the future space technologies, while Ecuador has its own prestigious space program specially on micro-gravity research and much more. Paraguay is getting ready to team up with the rest of the nations in the continent. Venezuela's situation is not conducive at present due to its internal politically turbulent situations. Regarding the three Guyanas, French Guyana already hosts launch facilities for rockets. Considering all these various developments, the time is ripe for a common space program getting initiated from Peru. Gradually , this program can be expanded to Bolivia, Chile, Ecuador, Colombia, Uruguay, Paraguay, Argentina and Brazil. Also, With the acquisition of the Earth Observation technology, Peru becomes the first Latin American country to have a satellite capacity to detect objects smaller than one meter.

"This success was made possible by the creation of the "Projects Factory©", a new and more integrated working organization in the Space System business unit in Airbus Defence and Space. This new way of working brings down development and construction lead times for satellites up to 500 kg and optimizes their costs and schedule delivery, without impacting quality in any way".

CONCLUSION AND FUTURE TRENDS

Peru is one of the foremost countries to accept responsibilities specially regarding space and aerospace technologies as the country highly values and understand the core importance of these advanced technologies for a prosperous society. Since SAGANS offers more features regarding satellites regarding vehicle and way-point navigation, airborne and seafloor mapping, precision farming, monitoring of natural resources, illegal mining, illegal activities, terrorism, smuggling, drug trafficking, forest mapping, utilities and retail industry, monitoring and advanced warning systems of natural calamities like earthquakes, Tsunamis, volcanic eruptions, cadastral surveying, structural deformations and other civil engineering applications and much more etc, the various universities that participated in the preparation of nanosatellites can begin with any theme listed above like vehicle navigation, weather monitoring, precision farming , seafloor mapping etc and can prepare nano-satellites in collaboration with CONIDA and other space agencies in the continent. SAGANS can prove to be a triggering gigantic project comprising a collection of space satellite projects , the various instruments to be mounted on each satellite to be launched. Although SAGANS has much in common with the Earth observation technology acquired by Peru from France ( Pleiades ), still SAGANS will be much more indigenous in nature and offers much more in comparison with the Earth Observation technology. The technical details will gradually be described in the consecutive papers in a systematic manner.

ACKNOWLEDGMENT

The author is highly indebted to Dr. Avid Roman Gonzalez and his team of engineers from INTI Labs, UCH, Lima, Peru for his highly valuable ideas and inputs towards a dedicated effort in trying to have a common space agency for the entire South American Continent, Space weather-GPS navigation and aerospace technologies being the common goals of the space agency in the near future. The author also expresses his gratitude to all the dedicated scientists and researchers in Latin America who are working towards these high goals. The author is extremely grateful to Dr. Ajey Lele , Senior Fellow of IDSA, India for his high motivational inputs.

Fig ( 1 )

 1 Fig (1) : The Lat-Long of South America ( Courtesy : Google images)

Fig ( 2 )

 2 Fig (2) : PeruSAT-1 ( Courtesy : Google images)

Fig ( 3 )

 3 Fig (3) : PUCP-Sat-1 & Pocket-PUCP ((http://inras.pucp.edu.pe/) UAPSAT-1 The Universidad Alas Peruanas -UAP also developed a nanosatellite called UAP-Sat. The UAP-Sat 1 was launched on January 2014, but the project started in 2010. The UAP-Sat 1 was developed using the standard CubeSat technology and has temperature sensors on board, and its principal mission is an educational platform.The UAP-Sat 1 was tested by NASA related to temperature, vacuum, and vibrations.The research team was led by Eng. Juan Carlos Marca and composed by other Peruvian professional and students.

Fig ( 6 )

 6 Fig[START_REF] Roman-Gonzalez | The UNSAAC Activities in Aerospace Development[END_REF]: Chasqui 1satellite in space (http://www.chasqui.uni.edu.pe/)


A N Smirnov
email: andreysxxxx@gmail.com

Deriving space-time in four-dimensional Euclidean space with no time and dynamics

published or not. The documents may come

Introduction

There are two principal models of the nature at current time. The first model tries to use aether, the second model is based on a vacuum and relativity. Ethereal theories have many problems which looks unresolvable, and there is only one main opportunity for derivation of theories. Is it possible to derive entirely new model of the nature, different from the first two? Hypothesis with such model is offered in this article.

Is it possible to derive in Euclidean space a hypersurface with a Minkowski space metrics? As S. Hawking, J. Ellis [1, p 55] show, in Euclidean space it is impossible to derive the refined hypersurface with a Minkowski spacetime metrics.

Is it possible to derive in Euclidean space a hypersurface with a metrics of the general theory of relativity? If it is impossible to derive more simple case, with a Minkowski space metrics, then it is obvious that it cannot be done.

The demonstration of impossibility to derive the enclosed hypersurface with a special theory of relativity metrics in Euclidean space appears convincing, seems like it cannot be disproved. Any demonstration is based on some provisions which are considered as true. If there is any possibility to call into question any of these provisions, then all conclusions, dependent on such provision, also become doubtful. The provision questioned in this article is realism. Time participates both in a Minkowski spacetime metrics and in metrics of a general theory of relativity. Therefore, before considering the offered model, let's consider what the time is. Time is the phenomenon the effects of which we constantly observe. The physics still does not know the nature of time, the existing description of time and its properties is phenomenological. Special and general theories of relativity have established dependence between time, space and gravitation. It shows that time is not the independent phenomenon, and has the connection with space and matter causing gravitation. The physics has established the properties of time. However, there is no knowledge why there is time, why time is unidirectional, whether there are time quanta, why time has one dimension and whether it is possible to travel to the past.

Whether the space, time, matter and time fields exist independently or are the manifestation of something more fundamental? Let's assume that at the fundamental level time does not exist. Let's consider the arising consequences of this assumption.

If at the fundamental level time does not exist, then there has to be no dynamics. Options when there is dynamics at the fundamental level, and time is emergent at the macrolevel, are difficult to call model with no time. More likely, such models can be called models with a numerous of times at the microlevel.

With absence of time and dynamics at the fundamental level the question now arises of how to coordinate it with dynamics and time observed in the nature.

Model of hypothesis

Let us assume that there is a four-dimensional Euclidean space with some fields. No time or dynamics. Thereby, the fields also have no dynamics. It also means full determinism.

Let us assume that in this space we can build a series of noncrossing hypersurfaces on which somehow it is possible to build the fields precisely coinciding with the fields observed by us. Also let us assume there is a continuous transformation of the fields state Ψ on one hypersurface of 𝐿 series to the fields state on another hypersurface 𝐿 ′ of the same series.

Each point on one hypersurface is mapped to some point on other hypersurface. As the transformation is continuous, there is a curve consisting of mapping points on intermediate hypersurfaces, connecting a point on an L hypersurface to a point on an L' hypersurface. Let's call this curve the line of evolution.

It is possible to say that fields on hypersurfaces evolve along this line.

Let us assume that the mapping of fields states on one hypersurface to the fields states on another hypersurface along the line of evolution corresponds exactly with the laws of physics observed by us, and the distance on this line serves as the time in the equations. In this case we can talk about the time vector, and this vector is tangent to the line of evolution.

At the level of fundamental four-dimensional space the preferred direction is absent, all directions are equal.

The question now arises of where time vector is directed.

In fundamental space there is no preferred direction. Thereby, this vector has to be directed in the most symmetric way concerning a hypersurface. For the case of hyperplane, the greatest symmetry achieved if time vector at each point of hyperplane is directed perpendicular to the hyperplane. For the hypersurface the greatest symmetry achieved if the time vector is directed perpendicular to the tangent hyperplane.

In such model of the hypothesis the question arises as to what the mind is.

Mind

Within the suggested model, I postulating that the mind is an epiphenomenon caused by the change of physical fields on hypersurfaces. Change occurs not in time, but in fundamental space which differs from observed space. Observed space correspond to space of hypersurfaces. It is necessary for observed threedimensional space that hypersurfaces also were three-dimensional.

The space, time and matter observed by us are the product of mind. Without observer they are mathematical abstraction. Thereby, objectively they do not exist, they exist subjectively.

The observed space-time I will call emergent space-time.

Anthropic principle

From the model of theory follows that the observer is necessary for existence of the Universe Thereby, the anthropic principle follows from the theory.

The anthropic principle was offered [START_REF]Idlis -Main features of the observed astronomical Universe as the characteristic properties of the inhabited space system // Izv[END_REF][3] for an explanation scientifically why in the observed Universe there is a number of nontrivial relations between fundamental physical parameters, necessary for existence of intelligent life, takes place. There are various formulations; usually the weak and strong anthropic principles are marked out.

The variant of the strong anthropic principle is the anthropic principle of participation stated by John Wheeler [START_REF] Wheeler | Genesis and Observership//Foundational Problems in the Special Sciences[END_REF]:

Observers are necessary to bring the Universe into being.

In the suggested model the anthropic principle of participation is a direct consequence of subjective existence of the observed space-time.

Principle of causality

All models of intelligent life known to me require the principle of causality. Observers are necessary to bring the Universe into being. Only the rational being can be the observer. It means that intelligent life is necessary to bring the Universe into being. Based on this, hypersurfaces with the physical fields changing on them need to be built so that the principle of causality was achieved. Thereby, the principle of causality is a consequence of the anthropic principle of participation.

Derivation of hypersurfaces and observer

The observer in the suggested model is that basis around which the emergent space-time is derived. There can be many observers on the same hypersurface. If for any observer a number of hypersurfaces is derived, it does not mean that the hypersurfaces are suitable for other observers. In this case, for some observers the subsequent hypersurfaces will differ.

Symmetry to the translations of the emergent time and space

To accomplish the principle of causality it is necessary to understand what properties in relation to translations of the emergent time and space physical laws have to have. In case there is no symmetry to the translations of the emergent time and space, there are no ways for accomplishment of the principle of causality. With that in mind, it follows that such symmetry, it is also could be called the uniformity, has to exist. It means that any decision with the emergent space-time has to contain such symmetries.

Observable physical fields

Observed physical fields, according to the suggested model, are some manifestation of more fundamental fields. Perhaps, they are a manifestation of the uniform field. Since this more fundamental fields or field are defined on space with no time and dynamics, they have no dynamics.

Inertial frames of reference

Let's call the inertial frames of reference the frames of reference moving directly and evenly relative to one another.

The question now arises of how to move from one inertial frame of reference into another. Let's consider a case when the emergent space is flat. In this case, instead of a hypersurface we can talk about the hyperplane.

If the body is motionless with regard to the hyperplane, then it evolves along time vector. If the body has any speed with regard to the hyperplane, then it evolves along the vector consisting of the sum of time and speed vector. Vectors of time and speed are perpendicular to each other as the vector of speed lies in the hyperplane. I want to find out how to move into the frame of reference corresponding to a moving body. As the motionless body evolves along time vector, the movement to frame of reference corresponding to a moving body would be the movement to such hyperplane where the speed is zero and a body evolves along time vector. For such movement it is necessary to make a turn of the hyperplane so that the time vector of the new hyperplane be parallel to a vector of time and speed of the body on the previous hyperplane.

Due to the consideration of movement from one frame of reference to another we get a number of the consequences.

The first consequence, relativity of simultaneity. The events occurring on the hyperplane are simultaneously occurring. After the hyperplane turn upon movement to the frame of reference corresponding to the body moving with some speed as to the previous earlier simultaneous events can cease to be simultaneous.

Other consequencethe observed difference of the clock rate in different frames of reference. As there is no preferred direction in fundamental space, the length corresponding to unit of time has to be constant and is not affected by turns. Before turn evolution of the body moving with some speed is characterized by the vector consisting of time vector with a length equal to unit of time, and the speed vector with a length depending on speed. After the turn and movement to system where a body is motionless, evolution of a body goes along time vector with a length corresponding to the unit of time. As we can see, lengths of these vectors differ, as means the difference of the clock rate in different frames of reference.

The consequence of similarity of laws of nature. As there is no preferred direction at the level of fundamental space, it means that in the emergent space-time physical laws are identical in all inertial frames of reference.

Energy

Within this model, the question arises as to what energy is. Suggested answer: energy is the first integral of motion equations. At the fundamental level there is no energy as there is neither time, nor the motion, nor dynamics.

Special theory of relativity and Lorentz transformation

Let's find ratio of the duration of time in two inertial frames of references, moving relatively to each other. I will name v t distance in fundamental space, equal to unit of time. As described above, this value is the same in all inertial reference systems.

Let there be two inertial frames of reference moving relative to each other with speed v along axis x, and their origin points coincide.

The figure above shows the axes x and t for first frame of reference and axes x ′ and t ′ for second frame of reference. The second frame of reference, moving with relative velocity v, is tilted at an angle α relative to the first. I would like to emphasize that the axis t is usual space axis in Euclidean space. Length l along this axis is related to the observed time by the following relation:

t = l/v t
Simultaneous events are those events that occur on a same plane, perpendicular to the axist.

There are several points in the figure. Point 1 is the beginning of the coordinate system. I consider case when the beginning of the coordinate system is same for both systems.

Because v t in all inertial frame of references is same, so v = v t sin(α) Let t be the time elapsed in the first reference frame from point 1, аnd t ′ -time elapsed in the moving reference frame during time t. Time duration t in first frame corresponds to the distance v t t, this is distance between points 1 and 4. Same time span t in second frame of reference corresponds to same distance, it is distance between points 1 and 5. Point 2 is the intersection of a line perpendicular to the axis t ′ , and passing through the point 5. Similarly, point 3 is the intersection of a line perpendicular to the axis t, and passing through the point 4. In order to determine which time interval in the first frame of reference corresponds to the time t ′ in second, it is necessary to find the length of the hypotenuse of a triangle of points 1, 5 and 2. From the figure it can be seen:

t = t ′ cos (α)
Then, from the known value of the sine, we get:

cos(α) = √1 -sin 2 (α) = √1 -( v v t ) 2 t = t ′ √1 -( v v t ) 2
From the same figure it can be seen:

t ′ = t cos (α) = t √1 -( v v t ) 2
Now consider the coordinate transformations and see how point (x, y, z, t) will be transformed. Let velocity v be directed along x axis. Then, when you rotate the coordinate system to switch to moving frame of reference, y and z will remain unchanged:

y = y ′ z = z ′
Then, with usage of same method as above:

x ′ = (x -vt) /cos(α) = x -vt √1 -( v v t ) 2 t ′ = t -(v/v t 2 )x √1 -( v v t ) 2
These equations become familiar if

v t = с
Here сlight velocity. This means that the distance corresponding to the unit of length of time is equal to the distance traveled by the light for the same time duration.

Thus, I can say that the special theory of relativity with its Lorentz transformations is derived from the proposed model.

Let's consider question of how to calculate sum of velocities and what it is. From the equations above one can derive the equation of the relativistic velocity addition. This equation is different from the velocity addition equation, which can be obtained if we consider the sum of the velocities through the addition of angles. Is this difference a problem for the proposed hypothesis?

To answer this question, it is necessary to remember that all physics in this hypothesis is built around an observer. The observer will see the addition of velocities in accordance with the relativistic formula for the addition of velocities. If there is another observer in the second frame of reference, he will see his picture of events, and nothing says that this picture should be derivable from the picture of the first observer. Based on the above, I can conclude that the transition to another frame of reference is not isomorphic. The violation of isomorphism during the transition to another frame of reference means that for accelerating observer his past changing.

Let's consider a thought experiment. Two observers decided to observe some phenomena in some spatial area. Both observers meet, each takes a clean notebook where they will record the results of the observations. Then the first observer remains in same area, the second at some vehicle accelerates to nearlight velocity. Each of them regularly records observable phenomena in the assigned region of space.

Then the second observer returns, meets with the first observer, and they compare the results recorded in notebooks. Can there be different results in notebooks? To answer this question, it is necessary to remember that the space-time in this hypothesis is built around the selected observer, and is built with the requirement to satisfy to principle of causality. Therefore, for each of the observers, what he sees in the notebook should satisfy the principle of causality. This means that while observers may record different events, the causality principle must be followed for them. This means that for any observer the events during the transitions to another inertial frame of reference look isomorphic. However, if in any way the observer could see events at the same time in different reference frame, he would see that events in different reference frames are not isomorphic with respect to each other.

Thus, the Lorentz transformations are derived without any assumptions about the presence of the maximum velocity of interactions in emergent spacetime. It follows from the Lorentz transformations that the maximum speed of interactions exists, it is same in all inertial frames of reference and is equal to the length of a unit of time.

Curved space-time and gravitation

In the deriving of hypersurfaces, the existence of curvature, in observance of the principle of causality and similarity of the occurred physical laws, can be required. Let's consider consequences of curvature on a hypersurface.

Let's consider curved hypersurface. In the figure below in horizontal direction you can see the distance along some line on a hypersurface, in vertical directioncurvature of a hypersurface. "A" point is marked in the figure. This hypersurface is mapped to the same or similar hypersurface located further in fundamental space.

"A" point will be mapped to points on the subsequent hypersurfaces which are over the intersection with the line of evolution of this point. In each point the time vector is tangent for this line. Then it is seen that in each subsequent point along the line of evolution of "A" point the tangent hypersurfaces will not be parallel. The curvature leads to the turn of the tangent hyperplane in fundamental space. According to the considered earlier, the hyperplane turn is equivalent to change of speed. Therefore, the gradual turn is equivalent to acceleration. It means that the curvature of space-time, from the point of view of moving with the "A" point observer and provided that inhomogeneity of curvature are rather small, is indistinguishable from acceleration. It is the same process of turn of the tangent hyperplane in fundamental space.

Thereby, existence of curvature leads to emergence in the emergent space of the effective field equivalent to acceleration. Also, it may be noted that effective fields in the emergent space are divided into two types:

 Fields which are some projection of fundamental fields on a hypersurface  Field formed as result of curvature of a hypersurface.

The field formed as result of a curvature at a hypersurface depends on all other effective fields. This dependence arises from the fact that this field forms in such way so that the principle of causality for other effective fields can be achieved. Thereby, we can say that this field is universal in the emergent space and interacts with all other effective fields. As this field depends on a configuration of other fields, the speed of its change has to precisely equal to the maximum speed of configuration change of the fields. This speed is equal to maximum speed of interactions.

The field with such properties is known. It is gravitation.

For gravitation the strong principle of equivalence holds. It was shown above that gravitation and acceleration are demonstration of the same process, the process of turn of the tangent hyperplane in fundamental space. Thereby, within the suggested model the strong principle of equivalence is derived. It is shown that its speed has to be equal with the maximum speed of interactions. This speed, as we know, is equal to the speed of light. It is shown that gravitation is a universal interaction. Also gravitation in such model depends only on other effective fields, but not on itself.

In the general theory of relativity gravitation complies with all the properties described above. For example, there is only an energy-momentum tensor of other fields in it, there is no energy-momentum tensor of gravitation. Gravitation has universal character, as is predicted by the suggested model.

It may be noted that the above difference in types of fields means that many approaches applicable and being efficient for fields of the first type, will not work in the second case. As it is observed in attempts to apply quantization to gravitation. Also I will note that in the suggested model there are no singularities at the level of fundamental space. Gravitation can result in gravitational singularities in the observed space, but at the same time in fundamental space singularities do not arise.

Conclusion

The hypothesis, based on subjective idealism, enabling to derive a space-time with a Minkowski spacetime metrics on Euclidean space with no time and dynamics is suggested. This hypothesis also allows deriving the curved space-time with a metrics of the general theory of relativity. It was demonstrated that the principle of causality and the anthropic principle arise from the hypothesis. It was demonstrated that the strong principle of equivalence of gravitation and acceleration arises from the hypothesis.

All principles and postulates on which special and general theories of relativity are based are being derived, Lorentz transformations were derived.