GOUSSEBAILE Arnaud

Economic losses from natural disasters have increased globally faster than GDP over the past 30 years due to population growth and low levels of prevention in exposed regions. Moreover, only one third of these losses are insured and the low penetration of insurance generates wealth shocks for the affected populations. In this context and in the perspective of climate change, reducing natural disaster losses and increasing insurance coverage have become major issues for our societies, which are addressed in this thesis. The low levels of prevention and insurance can be explained by numerous market imperfections and deficient public policies, as explained in the introductory chapter of the thesis. A better understanding of these market problems and the role of public policy is needed to improve them. Chapter 2 focuses on prevention choices in the context of city development. Using an urban economics model, it shows that riskier areas are developed near the city center than far from the city center, investment in building resilience develops more concentrated cities, and riskier areas are less densely populated and generate more prevention. Furthermore, insurance subsidies lead to excessive exposure to risk through increased density in the riskiest areas and an overall decrease in resilience. This analysis illustrates the negative effects of subsidies and the role that urban public policies such as density restrictions or building codes can play. The following chapters address the issue of risk sharing in the context of risk correlation, a major feature of natural disaster risk. Using an economic model with potentially correlated individual risks, Chapter 3 demonstrates that a Pareto-optimal risk allocation can be achieved with competing insurance companies and a limited number of financial assets. This result, which is valid without market imperfections, requires in particular that agents are fully liable for the contracts signed in each state of nature. In practice, to limit defaults in catastrophic states, public policy requires that agents have financial reserves. Chapters 4 and 5 focus on the problem of risk correlation when these reserves are costly. Chapter 4 studies how the probability of a risk affects the choice of coverage of exposed individuals. It shows that individuals are more likely to insure for low probabilities than for high probabilities with standard insurance costs, but that the result is reversed when costs due to financial reserves are added. Chapter 5 analyzes the optimal form of insurance contracts when individual risks are correlated in a community. It shows that the optimal contract consists of partial insurance against individual risk, with lower coverage in catastrophic states than in normal states, plus potentially dividends in normal states. The final chapter concludes by opening up new research questions related to disaster prevention and insurance.

Cities located in regions prone to natural hazards such as flooding are not uniformly exposed to risks because of sub-city local characteristics (e.g. topography). Spatial heterogeneity thus raises the issue of how these cities have spread and should continue to develop. The current paper investigates these questions by using an urban model in which each location is characterized by a transport cost to the city center and a risk exposure. Riskier areas are developed nearer to the city center than further away. Investment in building resilience leads to more compact cities. At a given distance to the city center, riskier areas have lower land prices and get lower household density and higher building resilience. Actuarially fair insurance generates optimal density and resilience. An increase of insurance subsidization leads to an increase of density in the riskiest areas and a general decrease of resilience. In this case density restrictions and building codes have to be enforced to limit risk over-exposure.

World economic losses due to natural disasters have increased faster than GDP in the last three decades because risky regions have sustained growing population and low prevention measures. Moreover, only a third of these losses are insured and the low penetration of insurance generates undesirable wealth fluctuation for affected population. In this context and in the perspective of climate change, reducing natural disaster losses and increasing insurance coverage have become main challenges for our societies, which are addressed in the present thesis. Low current levels of prevention measures and insurance coverage can be explained by the numerous market imperfections and poorly designed public policies, as detailed in the introductive chapter of the dissertation. It is thus crucial to better understand these market failures and the role of public policies to improve both of them. Chapter 2 investigates preventive behaviors in the context of city development. By featuring an urban model, it shows that riskier areas are developed nearer to the city center than further away, investment in building resilience leads to more concentrated cities and riskier areas get lower household density and higher building resilience. Moreover, insurance subsidy leads to risk over-exposure through increase of density in the riskiest areas and general decrease of resilience. This analysis highlights the negative effects of subsidization and the role that can be played by urban policies such as density restrictions and building codes. The following chapters deal with risk sharing in the context of risk correlation, a main feature of natural disaster risks. In a model of a risky economy with potential risk dependence between individuals, chapter 3 shows that Pareto optimal allocation of risks can be reached thanks to stock insurance companies in competition and a reduced number of financial assets. This result, which is valid without market imperfections, requires in particular that agents be fully liable for their contracts in each state of nature. In practice, to limit the default on liabilities in catastrophic states, public policies require agents to secure financial reserves. Chapters 4 and 5 investigate the issue of risk correlation when securing financial reserves is costly. Chapter 4 analyzes how the probability of a risk affects the purchase of insurance by risk-exposed individuals. It demonstrates that individuals are more inclined to insure for low-probability risks than for high-probability risks with standard insurance costs, but result is reversed when reserve related costs are added. Chapter 5 examines the optimal design of insurance contracts when individual risks are correlated in a community. It shows that the optimal contract consists in partial insurance against individual risk, with a lower indemnity in catastrophic states than in normal states, and potentially some dividend in normal states. The last chapter concludes by opening on further possible research related to prevention and insurance of natural disasters.

This thesis deals with prevention and insurance of natural disasters. Low current levels of prevention measures and insurance coverage are explained by numerous market failures and poorly-designed public policies. Modeling individual behaviors, markets and public policies, this thesis aims at characterizing prevention actions and insurance mechanisms that could mitigate efficiently losses and wealth variability for risk averse agents. Chapter 1 investigates preventive behaviors in the context of city development. It shows that risky areas are more developed nearer to the city center than further away and that investment in building resilience leads to more compact cities. This chapter also highlights the perverse effects of insurance subsidies leading to risk over-exposure and the role that can be played by urban policies such as density restrictions and building codes. The following chapters focus on insurance mechanisms when individual risks are not independent, a main feature of natural disaster risks. Chapter 2 shows that, without market failures, Pareto optimal allocation of risks is reached thanks to stock insurance companies in competition and a reduced number of financial assets. In practice, agents have limited liability and public policies require agents to secure financial reserves to limit payment defaults in catastrophic states. That is why chapters 3 and 4 investigate the issue of the cost of financial reserves. Chapter 3 analyzes how the cost of financial reserves affects the insurance demand of agents exposed to correlated risks. If the financial reserves for the collective risk leads to an additional premium in the price of insurance for one agent, it appears that for a given collective risk, the purchased coverage rate decreases when the individual probability of being affected decreases. Chapter 4 examines the optimal design of insurance contracts when individual risks are correlated in a community. If it is not costly for the community to build reserves, the optimal contract for a given individual risk consists in full coverage, whatever the collective losses, plus a dividend if necessary to redistribute the remaining part of the reserves. Otherwise, the optimal contract for a given individual risk consists in partial coverage when collective losses are high.