Harris Schlesinger

Putting Risk in Its Proper Place

This paper examines preferences toward particular classes of lottery pairs. We show how such concepts as prudence and temperance can be fully characterized by a preference relation over these lotteries. If preferences are defined in an expected-utility framework with differentiable utility, the direction of preference for a particular class of lottery pairs is equivalent to signing the nth derivative of the utility function. What makes our characterization appealing is its simplicity, which seems particularly amenable to experimentation.(This abstract was borrowed from another version of this item.)

Changes in Background Risk and Risk-Taking Behavior.

We consider the effects of changes in the distribution of a background risk on the optimal risk taking behaviour of a risk- averse decision maker. In particular, we suppose that the background risk deteriorates via a first- or second-degree stochastic dominance shift. Our contention is that such a change in background wealth should lead the individual to behave in a more risk-averse manner in decisions concerning any other independent risk. We examine conditions on preferences that are both necessary and sufficient for all FSD or SSD changes in background wealth to entail this property. These conditions place restrictions on the stronger measure of risk aversion defined by Ross [1981].

Optimal Insurance in Incomplete Markets

This paper examines the theory of optimal insurance purchasing in the presence of uninsurable background risk. Existing theorems concerning the optimal level of insurance and the optimal form of an insurance contract are shown to hold only under restricted market and risk assumptions. In particular, conditions sufficient for the optimality of full coverage or sufficient for the optimality of deductible policies depend on the correlation between insurable and uninsurable risks. These results may provide a partial explanation why existing theory is often contradicted by observable behavior.

A Good Sign for Multivariate Risk Taking

Decisions under risk are often multidimensional, where the preferences of the decision maker depend on several attributes. For example, an individual might be concerned about both her level of wealth and the condition of her health. Many times the signs of successive cross derivatives of a utility function play an important role in these models. However, there has not been a simple and intuitive interpretation for the meaning of such derivatives. The purpose of this paper is to give such an interpretation. In particular, we provide an equivalence between the signs of these cross derivatives and individual preference within a particular class of simple lotteries. (This abstract was borrowed from another version of this item.) (This abstract was borrowed from another version of this item.)

Rational Insurance Purchasing: Consideration of Contract Nonperformance

Much of the analysis of rational insurance purchasing and hedging strategies has been undertaken on the basis of the expected utility hypothesis. This decision framework has been used to reformulate the Bernoulli principle that a risk averter rationally would fully insure at a fair premium. Other applications include the analysis of insurance at unfair premiums (Mossin [1968 ] and Smith [1968]), the effects of state-dependent utility on the rational insurance purchase (Cook and Graham [1977]), the effects of risky background wealth (Doherty and Schlesinger [1983] and Mayers and Smith [1983]), and the design of the optimal insurance policy (Raviv [1979] ). Such analyses have been conducted on the assumption that insurance policies are free of insolvency (default) risk. This assumption stands in sharp contrast to the actuarial literature in which the insolvency risk, or probability of ruin, is a central focus of attention.

The Optimal Level of Deductibility in Insurance Contracts

This paper examines the choice of an insurance contract when insurance is of the deductible type. This optimal choice is shown to be directly related to the insureds degree of risk aversion. Under certain assumptions, it is shown that an individual with a higher loss probability, a higher degree of risk aversion, or a lower level of initial wealth will purchase more insurance. Conditions for the purchase of full coverage or no coverage are also examined.

The Theory of Insurance Demand

This chapter presents the basic theoretical model of insurance demand in a one-period expected-utility setting. Models of coinsurance and of deductible insurance are examined along with their comparative statics with respect to changes in wealth, prices and attitudes towards risk. The single risk model is then extended to account for multiple risks such as insolvency risk and background risk. It is shown how only a subset of the basic results of the single-risk model is robust enough to extend to models with multiple risks.

Arrow's Theorem on the Optimality of Deductibles: A Stochastic Dominance Approach

SummaryWe provide a new proof for the optimality of deductible insurance that does not depend on the expected-utility hypothesis. Our model uses only first- and second-degree stochastic dominance arguments.

Risk Aversion in Rent‐Seeking and Rent‐Augmenting Games

The effects of risk aversion are examined for two types of expenditures in rent-seeking contests: (1) rent-seeking expenditures, which improve the probability that the rent is obtained and (2) rent-augmenting expenditures, which increase the size of the rent to be awarded. Risk aversion is shown to reduce expenditures of type (2) unambiguously, while having an indeterminate effect on those of type (1). These two contrasting results are shown to derive from the very different effects rent-seeking and rent-augmenting expenditures have on the riskiness of a players position. Copyright 1997 by Royal Economic Society.

Multiplicative Background Risk

Although there has been much attention in recent years on the effects of additive background risks, the same is not true for its multiplicative counterpart. We consider random wealth of the multiplicative form xy, where x and y are statistically independent random variables. We assume that x is endogenous to the economic agent but that y is an exogenous and nontradable background risk that represents a type of market incompleteness. Our main focus is on how the presence of the multiplicative background risk y affects risk-taking behavior for decisions on the choice of x. We extend the results of Gollier and Pratt (1996) to characterize conditions on preferences that lead to more cautious behavior.