Moral Hazard and Insurance: Optimality, Risk and Preferences

Sammanfattning: The thesis consists of an introductory chapter, followed by three chapters which all deal with theoretical issues related to moral hazard and insurance. In Chapter 2 we assume symmetric and perfect information. We conclude that, given some standard assumptions, the expected utility function cannot be quasi-concave, which strengthens earlier findings in the literature. As a consequence convex preferences cannot be obtained, a fact that has far-reaching negative consequences for, among other things, the existence of a price equilibrium. A second result concerns the relation between risk and utility in traditionally employed models of moral hazard and insurance. We use the envelope concept to conclude that it is possible to increase the expected utility of an agent by increasing his exposure to risk, while holding fixed all other relevant variables of the model. Since the agents are assumed to be risk averse, this result is counter-intuitive and requires further clarification. Chapter 3 introduces asymmetric information, which implies that the behaviour of the insured cannot be observed. Our assumptions, which are different from those made earlier in the literature, are shown to be sufficient to validate the first-order approach, which means that the first order condition of the consumer problem can replace the incentive compatibility constraint, making the problem much more mathematically tractable. In the second part of the chapter we use basic differential geometry to conclude two existence and uniqueness results, concerning the relation between optimal contracts and the economy under asymmetric information. These results are made under the assumption of constant absolute risk aversion. In Chapter 4 we introduce an alternative prevention technology, describing the relation between precautionary effort and probability of an accident. The main argument is that a big risk (for example a flood) should be more expensive to prevent than a small risk (for example a bicycle theft). We thus include the risk level as a determinant of the probability of an accident. In turn, we use this new prevention technology to analyse the problems advanced in Chapter 2. Among other things, we find that it is now, indeed, possible to obtain convex preferences under reasonable assumptions, a result which has not been presented previously in the literature. Since many of the problems of moral hazard, as discussed in the introductory section, relates to non-convex preferences, this finding should be considered one of the most interesting results of the entire dissertation. In addition, we also analyse the implications of introducing the new probability function upon the relation between risk and expected utility. We conduct an analysis similar to the one carried out in Chapter 2, and conclude that the counter-intuitive result found in that chapter has now disappeared. Thus a higher risk always induces a lower utility, a result we find to be more consistent with intuition.