Béatrice Rey

Prevention and precaution

This chapter surveys the economic literature on prevention and precaution. Prevention refers as either a self-protection activity – i.e. a reduction in the probability of a loss – or a self-insurance activity – i.e. a reduction of the loss –. Precaution is defined as a prudent and temporary activity when the risk is imperfectly known. We first present results on prevention, including the effect of risk preferences, wealth and background risks. Second, we discuss how the concept of precaution is strongly linked to the effect of arrival of information over time in sequential models as well as to situations in which there is ambiguity over probability distributions.

Prudence, temperance, edginess, and risk apportionment as decreasing sensitivity to detrimental changes

This paper shows that the notions of prudence, temperance, edginess, and, more generally, risk apportionment of any degree are the consequences of the natural idea that the sensitivity to detrimental changes should decrease with initial wealth. In the setting of Epstein and Tanny (1980), this turns out to be equivalent to the supermodularity of the expected utility for some specific 4-state lotteries.

Priority setting in health care and higher order degree change in risk

This paper examines how priority setting in health care expenditures is influenced by the presence of uncertainty about the severity of the illness and the effectiveness of medical treatment. We provide necessary and sufficient conditions on social preferences under which a social planner will allocate more health care resources to populations at higher risk. Changes in risk are defined by the concept of stochastic dominance up to order n. The shape of the social utility function and an equity weighting function are used to model the inequality aversion of the social planner. We show that for higher order risk changes, the usual conditions on preferences such as prudence or relative risk aversion are not necessarily required to prioritise health care when there are different levels of uncertainty associated with otherwise similar patient groups.

On Non-Monetary Measures in the Face of Risks and the Signs of the Derivatives

Vulnerability of both prudence and temperance towards a sure loss and towards a zero-mean background risk seems to be a very realistic assumption on individual preference. This paper shows that when the concepts of prudence and temperance are defined in non-monetary terms, the above assumption is equivalent to the usual signs of the successive derivatives of the utility function.

On Ambiguity Apportionment

This paper investigates the notion of changes in ambiguity over loss probabilities in the smooth ambiguity model developed by Klibanoff, Marinacci and Mukerji (2005). Changes in ambiguity over loss probabilities are expressed through the specific concept of stochastic dominance of order n defined by Ekern (1980). We characterize conditions on the function capturing attitudes towards ambiguity under which an individual always considers one situation to be more ambiguous than another in a model of two states of nature. We propose an intuitive interpretation of the properties of this function in terms of preferences for harms disaggregation over probabilities, also labelled ambiguity apportionment.

Decision Thresholds and Changes in Risk for Preventive Treatment

This paper investigates the notion of treatment threshold for preventive treatment with potential side effects in the context of changes in risk. Changes in risk are defined by the concept of nth-order stochastic dominance and concern the effectiveness of preventive treatment, side effects, severity of the potential disease, and comorbidity risk. The impact of a riskier environment on the probability of disease threshold above which the preferable decision is to undergo preventive treatment is shown to depend on both mixed risk averse individual preferences and the configuration of increase in risk considered. These results suggest that neglecting differences between risks when evaluating the treatment threshold is likely to lead to substantial errors in most cost-benefit applications for preventive treatment.

Preserving preference rankings under non-financial background risk

AbstractWe investigate the impact of a non-financial background risk 𝜀̃ on the preference rankings between two independent financial risks 1 and 2 for an expected-utility maximizer. More precisely, we provide necessary and sufficient conditions for the alternative (x0+1,y0+ 𝜀̃) to be preferred to (x0+2,y0+ 𝜀̃) whenever (x0+1,y0) is preferred to (x0+2,y0). Utility functions that preserve the preference rankings are fully characterized. Their practical relevance is discussed in light of recent results on the constraints for the modelling of the preference for the disaggregation of harms.