Contributions to Insurance Economics

This paper reviews the economic theory of risk-sharing. We focus on the link between models with a complete set of markets for contingent claims and the theory of optimal insurance. Accordingly, an insurance contract can be viewed as a bundle of contingent goods. Transaction costs are shown to be the driving force for deductibles. Coinsurance can be due to either insurers’ risk aversion or nonlinearity in administrative costs. We conclude that insurance markets seem to be inefficient in that they do not satisfy the mutuality principle, a property of efficient contingent allocations.

The demand for and supply of liability insurance arise from the legal liability of individuals and corporations for injuries caused to third parties. Tort liability rules and liability insurance markets have attracted substantial attention in recent years. This paper introduces the literature on the demand for and supply of liability insurance. The focus is on issues that distinguish liability from first party insurance. Particular emphasis is given to the relationships between liability law, liability insurance, and risk reduction.

This essay synthesizes and extends the theory of optimal insurance under moral hazard, with a focus on the form of insurance contracts. The simplest model illustrates the most fundamental result: that the market responds to moral hazard with partial insurance coverage. But this model is not general enough to predict the contractual form of this response. The most general model, the Principal-Agent model, yields mostly negative results. In extending the theory, I adopt an intermediate approach, distinguishing between moral hazard on the probability of an accident and moral hazard on the size of the loss. This approach generates predictions as to when deductibles, coinsurance and coverage limits will be observed. The essay reviews as well moral hazard with a partially informed insurer and dynamic models of moral hazard. It concludes with a discussion of open questions in the theory of moral hazard and insurance.

In this survey we present some of the more significant results in the literature on adverse selection in insurance markets. Section 1 discusses the monopoly model introduced by Stiglitz (1977) for the case of single period contracts and extended by many authors to the multi-period case. The introduction of multi-period contracts raises many issues that are discussed in detail: time horizon, discounting, commitment of the parties, contract renegotiation, and accident underreporting. Section 2 covers the literature on competitive contracts. The analysis becomes more complicated since insurance companies must take into account competitive pressures when they set incentives contracts. As pointed out by Rothschild and Stiglitz (1976), there is not necessarily a Cournot-Nash equilibrium in presence of adverse selection. However, market equilibrium can be sustained when principals anticipate competitive reactions to their behavior or when they adopt strategies that differ from the pure Nash strategy. Multi-period contracting is discussed. We show that different predictions on the evolution of insurer profits over time can be obtained from different assumptions concerning the sharing of information between insurers about individual’s choice of contracts and accidents experience. The roles of commitment and renegotiation between the parties to the contract are important. We then discuss how risk categorization can be used to improve resource allocation under adverse selection. Finally, the last section introduces models that simultaneously consider moral hazard and adverse selection. A short conclusion summarizes the main results in recent literature and discusses some avenues of future research.

Insurance companies are levered corporations that borrow money by issuing a specific type of debt instrument, the insurance policy. Insurance debt is more risky than conventional debt because neither the amount nor the timing of the debt repayments are known in advance. The debt analogy suggests financial modeling as a natural approach to the pricing of insurance. This paper reviews the theory of financial pricing of insurance and proposes some extensions. The review covers the insurance capital asset pricing model CAPM, discounted cash-flow models, and option pricing models. The extensions include an option model of the insurance firm allowing for multiple asset and liability classes and an analysis of insurance company equity as a down-and-out option.

This paper deals with the econometrics of car accidents, that is, the estimation of the relative importance or significance of the factors explaining the number of accidents in a given period on an individual basis. The number of car accidents is a discrete variable and, therefore, represents a count process: the dependent variable takes only nonnegative integer values. Hence, the observed dependent variable is the number of accidents an individual i had in the period considered. The individual characteristics are considered exogenous or predetermined and may or may not be significant factors in explaining the number of accidents. We have estimated four categorical models (linear probability, probit, logit, and multinomial logit) and four count data models (Poisson and negative binomial models with and without individual characteristics in the regression component). It is difficult to compare the econometric results of the different models since some of these models are not nested. However, it is shown that the negative binomial model with a regression component produces a reasonable approximation of the true distribution of accidents. Different statistical tests reject the Poisson models (with and without a regression component) and the negative binomial model without individual characteristics. It is also observed that all estimated models provide the same qualitative results (essentially the same significant variables), but differ when predictions of either the probabilities of accident or the expected number of accidents were made. For quantitative predictions, it is important to select the appropriate model. Moreover, it is shown that, in all models, the individual’s past driving experience is a good predictor of risk. Finally, we apply the statistical results to a model of insurance rating in the presence of moral hazard.