Louis Eeckhoudt

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].

Background Risk, Prudence, and the Demand for Insurance

This paper addresses the question of whether uninsurable background risk will lead people to buy more insurance against other risks that are insurable. The conditions of decreasing absolute risk aversion and decreasing absolute prudence on the utility function and either statistical independence or a general condition indicating a positive relationship between the background risk and the other risk are shown to be enough to guarantee that background risk will increase the optimal amount of insurance against the other risk. In particular, background risk raises the optimal coinsurance rate and reduces the optimal level of the deductible (for any given coinsurance rate).

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.)

Background Risks and the Value of a Statistical Life

We examine the effects of background mortality and financial risks on an individuals willingness to pay to reduce his mortality risk (the value of statistical life or VSL). Under reasonable assumptions about risk aversion and prudence with respect to wealth in the event of survival and with respect to bequests in the event of death, background mortality and financial risks decrease VSL. The effects of large mortality or financial risks on VSL can be substantial, but the effects of small background risks are negligible. These results suggest that the commonplace failure to account for background risk in evaluating VSL is unlikely to produce substantial bias in most applications.

Demand for Risky Assets and the Monotone Probability Ratio Order

Since Fishburn and Porter (1976), it has been known that a first-order dominant shift in the distribution of random returns of an asset does not necessarily induce a risk-averse decision maker to increase his holdings of that improved asset. To obtain the desired comparative statics result, one has to further restrict the class of changes in the distribution. In this article, we propose the “monotone probability ratio” criterion which is more general than the “monotone likelihood ratio” criterion currently used in the literature.

Insurance and Saving: Some Further Results

Abstract The purpose of this paper is to provide a joint treatment of the saving and insurance decisions which have very often been dealt with separately in the economic literature. In the present model any decrease in the current consumption level can be used to finance either insurance purchase or an increase in the stock of safe assets held in financial institutions (called ‘deposits’ or ‘contingency reserves fund’ for brevity). The most important result is that, under decreasing temporal risk aversion, deposits and insurance are pure substitutes in the Hicksian sense. Besides, it is shown among other comparative statics results that insurance is not necessarily an inferior good, contrarily to the prevailing view in the literature. Finally, we indicate under which conditions a separation theorem between consumption, insurance and deposits holds. These conditions are either a fair insurance premium or a constant temporal risk aversion. Finally our results are compared to related ones in the literature.

Risk-aversion, prudence and temperance: A unified approach

Risk aversion can be defined either by the negative sign of the second derivative of the utility function or by the rejection of any mean-preserving increase in risk. The more recent notions of prudence and temperance have so far been defined exclusively by the sign of the third and the fourth derivative of the utility function. In this paper we show that, as risk aversion, prudence and temperance can also be interpreted as systematic attitudes towards transformation of a density function.

The no-loss offset provision and the attitude towards risk of a risk-neutral firm

In this paper, we show how a differentiated tax treatment of corporate losses and corporate profits induces the firm to behave in a very specific risk-averse manner.

Increases in risk and deductible insurance

Abstract This paper examines how mean-preserving transformations in the loss distribution affect the optimal level of deductibility in an insurance contract. If marginal utility is convex, increases in risk affecting losses only below the deductible are shown to lead to a reduction in coverage (higher deductible), which can be viewed as an increase in precautionary savings. On the other hand, a transformation that spreads losses more towards the tails of the distribution leads to an increase in coverage (lower deductible) whenever preferences exhibit nonincreasing absolute risk aversion.