BARRIEU Pauline

This doctoral dissertation focuses on the modeling of preventive effort and its relationship with market insurance. Each chapter attempts to capture different aspects of this problem, from the study of a criterion consistent with actuarial practices to the study of the supply side of insurance, including risk perception biases and an approach to prevention in dynamic time. Chapter 1 models the relationship between an insurer and an insured as a Stackelberg game. In this game, the insurer plays first by offering an insurance contract in the form of a loading factor. The insured then plays by choosing the optimal coverage rate and prevention effort. Both the insured and the insurer aim to minimize their respective risk measures, which are both consistent. The respective effects of self-insurance and self-protection on risk minimization will be studied. In each case, it will be shown that optimal choices for the insured exist and the optimal contract for the insurer will be characterized. Moreover, it will be shown that if the agent's risk measure decreases faster than his loss expectation, then the optimal effort is increasing with the loading factor with a potential discontinuity when the optimal coverage goes from full to zero. However, in the opposite case the optimal effort can be increasing or decreasing with the loading factor. Chapter 2 studies the relationship between self-insurance and market insurance also in the form of an optimization problem for one agent. Similar to Chapter 1, this agent must determine the coverage rate and the prevention effort that will optimally reduce its risk measure. The considered risk measure is called distortional and is defined from a non concave distortion function. This allows for potential individual cognitive biases in risk perception. The characterization of the optimal solution for the agent makes it possible to draw a new conclusion about the relationship between self-insurance and market insurance. Self-insurance is no longer just a substitute for market insurance, but can also be complementary to it, depending on the sensitivity of the prevention effort to the price of insurance. Chapter 3 focuses on self-protection by proposing a dynamic expected utility maximization problem. This takes the form of a stochastic control problem in which the agent chooses his insurance coverage and his prevention effort which is dynamic. The problem can be separated into two subproblems, the first one is an optimization in effort and the second one in insurance coverage. Since the individual wants to obtain the largest possible final wealth, he seeks to maximize the exponential utility expectation of this wealth. The agent's wealth can be seen as the solution of a backward-looking stochastic differential equation with a jump, this equation admits a unique solution and is moreover explicit. In particular, we obtain that the optimal self-protection effort is constant. The initial distribution of the loss process, when there is no effort, is given by a compound Poisson process which is in particular a Lévy process. Obtaining a constant optimal effort means that the Lévy property of the processes is preserved by maximizing an exponential utility expectation. The analysis of the problem in insurance coverage gives a sufficient condition to obtain the existence of an optimal level of coverage. The individual can then subscribe to an insurance policy by providing a preventive effort that will maximize his satisfaction or choose not to subscribe to the policy but by taking part in self-protection actions.

The remediation of contaminated sites is often subject to substantial cost overruns. This persistent discrepancy between estimated and realized costs is chiefly responsible for misguided land use and wasteful delays in the reconversion of former industrial sites. In order to deal with incomplete information and uncertainty in this context, this paper draws on stochastic modeling and mathematical finance methods. We show that relatively simple and usable formulas can then be derived for better assessing cleanup strategies. These formulas apply to generic remediation technologies and scenarios. They are robust to misspecification of key parameters (like the effectiveness of a prescribed treatment). They also yield practical rules for decision making and budget provisioning.

This volume is dedicated to the memory of Marc Yor, who passed away in 2014. The invited contributions by his collaborators and former students bear testament to the value and diversity of his work and of his research focus, which covered broad areas of probability theory. The volume also provides personal recollections about him, and an article on his essential role concerning the Doeblin documents. With contributions by P. Salminen, J-Y. Yen & M. Yor. J. Warren. T. Funaki. J. Pitman& W. Tang. J-F.

In this thesis, we study storm coverage dedicated to wind damage and a development of behavioral insurance through automobile risk. We combine external information such as wind speed with insurance data. We propose the construction of a storm index to complete and reinforce the evaluation of damages caused by major storms. We then define a division of the French territory into 6 storm zones, depending on the extreme wind correlations, to test several scenarios. These different tests and considerations allow us to improve our storm index. We use extreme value theory models to show the impact of variability on the calculation of return periods and capital requirements. We thus highlight the difficulties encountered in obtaining robust results in relation to extreme events. In the case of motor insurance, we test different methods to respond to technical and regulatory changes. We characterize the male/female partition using the logistic procedure, multiple correspondence analysis or classification trees. We show that it is possible to compensate for the absence of the gender variable by other information specific to the insured or to his vehicle and in particular the use of mileage records. Finally, we are interested in the experience acquired by novice drivers. We study the on-road behavior of the insured to create new risk classes.

Presentation of climate derivatives.

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