PANNEQUIN Francois

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In the first two chapters, we study the optimal contract problem in the presence of risk and ambiguity in the context of an optimal control problem. Ambiguity is modeled according to Klibanoff et al. (2005). Our approach generalizes the analyses performed so far by considering the insurance contract as a pair of a premium and an indemnity function to be solved simultaneously. We prove the existence of an optimal contract in the most general case where all agents can be simultaneously averse to ambiguity and risk, which includes all the cases previously considered. We characterize not only the risk sharing but also the ambiguity sharing rule between the contracting parties. In the case of unilateral ambiguity aversion, we show that a direct franchise policy cannot be an optimal insurance contract. Instead, under the assumption that conditional densities can be ranked according to the monotonic likelihood ratio, a contract with vanishing deductibles is optimal, a result that is consistent with Gollier (2014). In particular, the implemented methodology complements Raviv's (1979) analysis for the pure risk case with a risk-neutral insurer, showing that an upper limit coverage cannot be an optimum. This result is robust to ambiguity neutrality.In the third chapter, I examined the impact of risk and ambiguity on optimal investment in human and physical capital using the two-period Ben-Porath (1967) model. Uncertainty (both in the sense of risk and ambiguity) is introduced to human capital accumulation in two ways. When uncertainty is about the rate of depreciation of human capital (uncertain obsolescence of skills), I found that the optimal investment in human capital always increases regardless of whether physical capital is present. This response to uncertainty in a household represents typical self-insurance behavior. In contrast, when the uncertainty is about the efficiency of human capital accumulation, the optimal investment in human capital decreases among households with constant relative risk aversion less than one. This response to uncertainty is typical of a household that views investment as an asset with a risky return instead of insurance.The final chapter (relatively independent of the previous chapters) examines an important issue in growth theory: the role of renewable resources and externalities in the economy. The introduction of a regenerative function (of a natural resource) that is non-concave with respect to one of the arguments makes the problem non-convex. As a consequence, we can no longer use traditional dynamic programming techniques. By attacking this problem, we propose a new method to study a two-sector economy in the presence of externalities. In this case, we introduce the concept of "net stock gain", which is a notion similar to the "net investment gain" introduced by Kamihigashi et al. (2007). In the absence of the usual convex or supermodular properties, we prove that the economy evolves to increase the net stock gain and establish the conditions ensuring the convergence of the economy in the long run. This approach can be applied to similar problems posed above, or be extended to the analysis of multi-sector economies in general.

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An insurer can monitor the policyholder's prevention effort when it is observable ex-post by using a contract clause. The literature on insurance contracts does not explicitly address the role of contract clauses. We examine the role of such clauses in case of self-insurance. Because of the substitutability between insurance and self-insurance, contract clauses focused on self-insurance investments could cause a possible deterrent effect on insurance demand, highlighting their puzzling nature. In a theoretical model, we examine two arguments to overcome the compulsory self-insurance clause paradox: the observability of the self-insurance investment and the role of the self-insurance clause on insurance demand. The fact that self-insurance investments are not observable ex-ante cannot justify the use of a mandatory clause. Neither the demand for insurance nor the demand for prevention is observability-dependent. Therefore, self-insurance clauses are, at best, useless, at worst, counterproductive: when binding, they reduce the size of the insurance market.

Key message Insurance might be an efficient tool to strengthen adaptation of forest management to climate change. A theoretical model under uncertainty is proposed to highlight the effect, on adaptation decisions, of considering adaptation efforts in forest insurance contracts. Results show that insurance is relevant to increase adaptation efforts under some realistic conditions on forest owner's uncertainty and risk preferences, and on the observability or not of adaptation efforts. Context One of the challenges of forest adaptation to climate change is to encourage private forest owners to implement adaptation strategies. Aims We suggest the analysis of forest insurance contracts against natural hazards as a vector to promote the implementation of adaptation efforts by private forest owners. Methods We propose a theoretical model of insurance economics under risk and under uncertainty. Results Our results indicate that when climate change makes the probability of the occurrence of the natural event uncertain, then it may be relevant to include adaptation efforts in the insurance contract, leading to an increase in the adaptation efforts of risk- averse and uncertainty-averse forest owners. In addition, we show that the relevance of insurance as a vector to promote adaptation efforts is greater when the forest owner's effort is unobservable by the insurer as compared to a situation of perfectly observable effort. Conclusion Under some realistic assumptions, the forest insurance contract seems to be a relevant tool to encourage forest owners to adapt to climate change.

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• Key message Insurance might be an efficient tool to strengthen adaptation of forest management to climate change. A theoretical model under uncertainty is proposed to highlight the effect, on adaptation decisions, of considering adaptation efforts in forest insurance contracts. Results show that insurance is relevant to increase adaptation efforts under some realistic conditions on forest owner’s uncertainty and risk preferences, and on the observability or not of adaptation efforts. • Context One of the challenges of forest adaptation to climate change is to encourage private forest owners to implement adaptation strategies. • Aims We suggest the analysis of forest insurance contracts against natural hazards as a vector to promote the implementation of adaptation efforts by private forest owners. • Methods We propose a theoretical model of insurance economics under risk and under uncertainty. • Results Our results indicate that when climate change makes the probability of the occurrence of the natural event uncertain, then it may be relevant to include adaptation efforts in the insurance contract, leading to an increase in the adaptation efforts of risk-averse and uncertainty-averse forest owners. In addition, we show that the relevance of insurance as a vector to promote adaptation efforts is greater when the forest owner’s effort is unobservable by the insurer as compared to a situation of perfectly observable effort. • Conclusion Under some realistic assumptions, the forest insurance contract seems to be a relevant tool to encourage forest owners to adapt to climate change.

In many insurance contracts, self-insurance clauses appeared. Our objective is to analyze if these self-insurance clauses are justified, function of the observability or not of the self-insurance by the insurer. For this purpose, we propose a theoretical model under risk and ambiguity jointly analysing insurance and self-insurance. Theoretical results show that self-insurance clauses are never justified under risk, and not justified under ambiguity when the self-insurance is observable by the insurer. Moreover, under ambiguity, when the self-insurance is unobservable by the insurer, we show that optimal self-insurance depends on ambiguity preferences. Our results also indicate that insurance and self-insurance are substitutes under risk and under ambiguity only when the self-insurance is observable by the insurer. Under ambiguity, when the self-insurance activity is unobservable, insurance and self-insurance may be or not substitutes when the decision maker has ambiguity aversion.

The auto insurance industry is facing a number of regulatory, financial, behavioral and technological changes. In order to face the challenges resulting from these changes and maintain their profitability, insurers must innovate in terms of pricing. In this context, we develop in this thesis two themes related to automobile insurance pricing. The first theme is based on the optimization of pricing strategies, both in underwriting and renewal. The second theme is oriented towards the use of experiments in order to better understand the determinants of insurance demand. We illustrate how empirical demand models based on data available to the insurer can be used to optimize profitability and customer retention. We then extend the optimization framework by taking into account the inter-temporal dependencies between current rate decisions and profits generated in future periods. Thus, we introduce the Customer Value framework that allows the insurer to adapt its pricing strategy according to policyholders' behaviors over their customer lifetime while taking into account the market cycle. The empirical illustrations in the first two chapters are based on natural data observed by the insurer.In the second part of the thesis, we illustrate the contribution of field and laboratory experiments to the understanding of the demand for automobile insurance. A field experiment allows us to refine the measurement of customer price elasticity and to treat the pricing problem as a contextual bandit problem. Offline evaluation of several reinforcement learning strategies shows that those applying targeted fare experimentation achieve better financial performance compared to the myopic strategy, which excludes any possibility of experimentation. Finally, we present the results of a laboratory experiment whose objective was to measure the added value of private variables from decision models in risk. In particular, we analyze the role of risk aversion and risk perception in explaining car insurance choices. The same experimentation allowed us to analyze the external validity in experimental insurance, i.e. the similarity of individuals' behaviors in an experimental context and in the real economic context of the market.In addition to the experimentation-optimization duality in the field of insurance pricing, this thesis thus illustrates the duality between private data and public data, as well as the duality between empirical models of insurance demand and theoretical models.

This work proposes an experimental approach to insurance fraud. We first present the two main paradigms that have been developed in the economic literature to analyze insurance fraud from a theoretical point of view: costly verification mechanisms and costly falsification mechanisms. According to the costly verification hypothesis, the insurer verifies claims by incurring an audit cost. This procedure can be deterministic or random. Under the falsification assumption, the insured incurs some cost to make the audit imperfect. The insurer is therefore unable to detect fraud with certainty. In parallel to this modeling, the experimentation carried out in these contexts confirms that the random audit dominates the deterministic audit and that the application of a severe penalty can deter fraud, mitigate the extent of falsification and compensate for the poor quality of the audit.

The standard theory of insurance demand, based on risk aversion on the part of the insured, predicts full insurance under actuarial premiums or partial insurance, i.e. full insurance beyond the deductible, in the presence of proportional loading (arrow, 1965). Faced with the various paradoxes that have come to light since that date, an alternative, innovative approach, based on the insurance application of the multi-risk market concept, developed in the early 1980s (doherty et al. In the face of the various paradoxes that have been uncovered since then, an alternative, innovative approach, based on the insurance application of the multi-risk market concept, was developed in the early 1980s (doherty and schlesinger (1983, 1985), eeckhoudt, gollier, schlesinger (1991), villeneuve and koehl (1996). . ). It allows to extend the spectrum of market solutions by taking into account the multiplicity of risks incurred by the insured. Our work uses these new theoretical developments to better understand social insurance systems. In the presence of anti-selection among insureds, linked contracts emerge: they allow us to illustrate the financing transfers at work in social protection. Moreover, compulsory markets appear to have different impacts on the demand for voluntary insurance by individuals, depending on their membership of a risk category and on the correlations in force between the sources of risk. Moreover, when policyholders differ only in their initial wealth, we draw all the consequences, in the complementary markets, of four types of redistribution at work in the compulsory markets: redistribution in price and quantity on the one hand, redistribution between policyholders and between periods on the other, by introducing temporal preferences as a characteristic of policyholders.

The validity of the utility expectation principle is considered in its application to the economics of insurance. The main results of the theory of insurance demand, in the presence of a single risk, are demonstrated in a simplified context. Several contradictory experiments on insurance choices are identified. However, it is shown that for a consumer faced with two insurable risks, the preference for insuring small frequent losses and over-insuring in actuarially unfavorable terms are no longer paradoxical. The theory of insurance markets in the presence of adverse selection highlights the deficiencies of market regulation. The application of this theory to social security legitimizes compulsory insurance systems. Redistribution then results from asymmetric information. It is shown that in insurance markets with asymmetric information, any second-best optimum can be achieved through a two-stage insurance mechanism. The first is compulsory partial insurance with the same price and benefits for all, and redistribution across risk classes. The second is supplementary coverage at an actuarial price for each type of risk. In this context, as soon as public insurance coverage exceeds a certain threshold, the existence and efficiency of this two-stage equilibrium is guaranteed. The analysis is extended to the classification of risks.