Greater downside risk aversion in the large

In this paper, we advance a definition of greater downside risk aversion that applies to both large and small changes in risk preference, and thereby complements the results for small changes reported previously. We show that a downside risk-averse transformation of a utility function results in a function that is more downside risk averse in the same manner that a risk-averse transformation increases risk aversion. Our demonstration is conducted first by using the compensated approach introduced by Diamond and Stiglitz [P. Diamond, J. Stiglitz, Increases in risk and in risk aversion, J. Econ. Theory 8 (1974) 337-360] and then by using an adaptation of the risk premium approach taken by Pratt [J. Pratt, Risk aversion in the small and in the large, Econometrica 32 (1964) 122-136].     

A note on comparative downside risk aversion

We provide comparative global conditions for downside risk aversion, which are similar to the ones studied by Ross for risk aversion. We define a coefficient of downside risk aversion, and study its local properties.     

Convex and decreasing absolute risk aversion is proper

Proper risk aversion, a pivotal concept in the study of behavioral conditions on utility functions, states that an undesirable risk can never be made desirable by the presence of an independent risk. It is well known that standard risk aversion is sufficient for this concept. We show in this short article that convex and decreasing absolute risk aversion is an alternative sufficient condition.     

An optimal auction with correlated values and risk aversion

We consider an auction setting where the buyers are risk averse with correlated private valuations (CARA preferences, binary types), and characterize the optimal mechanism for a risk-neutral seller. We show that the optimal auction extracts all buyer surplus whenever the correlation is sufficiently strong (greater than 1/3 in absolute value), no matter how risk averse the buyers are. In contrast, we note that a sufficiently risk-averse seller would not use a full rent extracting mechanism for any positive correlation of the valuations even if the buyers were risk neutral.     

Substituting one risk increase for another: A method for measuring risk aversion

This paper defines the rate of substitution of one stochastic change to a random variable for another. It then focuses on the case where one of these changes is an nth degree risk increase, and the other is an m  th degree risk increase, where n>m?1$n>m?1$. The paper shows that the rate of substitution for these two risk increases can be used to provide a broader definition and two additional characterizations of the nth degree Ross more risk averse partial order. The implications for local intensity measures of nth degree risk aversion are also examined. The analysis organizes the existing results as well as generates new ones.     

Housing and relative risk aversion

This paper derives closed-form and numerical solutions for relative risk aversion in a standard consumption-based model enriched with housing. The presence of housing enables the household to hedge against unexpected shocks and may decrease relative risk aversion. In addition, housing may generate state-dependent, time-varying risk aversion.     

The impact of prudence on optimal prevention revisited

We re-examine the link between absolute prudence and self-protection activities. We show that the level of effort chosen by an agent with decreasing absolute prudence is larger than the optimal effort chosen by a risk-neutral agent if the degree of absolute prudence is less than a threshold that is utility-independent and empirically verifiable.     

Survey measures of risk aversion and prudence

This paper utilizes a thought experiment conducted by the Bank of Italy to estimate absolute and relative risk aversion along with absolute and relative prudence for a broad cross-section of Italian households. Upper and lower bounds are calculated for each parameter, and comparisons are made across socio-demographic groups. Evidence is found of decreasing absolute risk aversion, decreasing absolute prudence, increasing relative risk aversion, and increasing relative prudence.     

Parametric characterizations of risk aversion and prudence

Summary. Our first main result says that whether one decision maker is more risk averse than another can be determined from their attitudes toward a given two-parameter family of risks. When all risks belong to this family, risk aversion can be compared even when initial wealth is random. Our second main result solves a long-standing problem in mean-variance analysis: what is the interpretation of the concavity of utility as a function of mean and variance? We show that in the case of normal distributions, this utility function is concave if and only if the agent has decreasing prudence. Received: July 29, 1996; revised: October 2, 1998     

Representative consumer's risk aversion and efficient risk-sharing rules

We study the representative consumer's risk attitude and efficient risk-sharing rules in a single-period, single-good economy in which consumers have homogeneous probabilistic beliefs but heterogeneous risk attitudes. We prove that if all consumers have convex absolute risk tolerance, so must the representative consumer. We also identify a relationship between the curvature of an individual consumer's individual risk sharing rule and his absolute cautiousness, the first derivative of absolute risk-tolerance. Furthermore, we discuss some consequences of these results and refinements of these results for the class of HARA utility functions.     

Mean-dispersion preferences and constant absolute uncertainty aversion

We axiomatize, in an Anscombe–Aumann framework, the class of preferences that admit a representation of the form V(f)=μ−ρ(d)$V(f)=\mu -\rho (d)$, where μ is the mean utility of the act f with respect to a given probability, d   is the vector of state-by-state utility deviations from the mean, and ρ(d)$\rho (d)$ is a measure of (aversion to) dispersion that corresponds to an uncertainty premium. The key feature of these mean-dispersion   preferences is that they exhibit constant absolute uncertainty aversion. This class includes many well-known models of preferences from the literature on ambiguity. We show what properties of the dispersion function ρ(⋅)$\rho (\cdot )$ correspond to known models, to probabilistic sophistication, and to some new notions of uncertainty aversion.     

More on parametric characterizations of risk aversion and prudence

Summary. This note provides an alternative proof for the equivalence of decreasing absolute prudence (DAP) in the expected utility framework and in a two-parametric approach where utility is a function of the mean and the standard deviation. In addition, we elucidate that the equivalence of DAP and the concavity of utility as a function of mean and variance, which was shown to hold for normally distributed stochastics in Lajeri and Nielsen [4], cannot be generalized. Received: November 27, 2000; revised version: November 26, 2001 Correspondence to: T. Eichner     

An index of loss aversion

To a considerable extent, risk aversion as it is commonly observed is caused by loss aversion. Several indexes of loss aversion have been proposed in the literature. The one proposed in this paper leads to a clear decomposition of risk attitude into three distinct components: basic utility, probability weighting, and loss aversion. The index is independent of the unit of payment. The main theorem shows how the indexes of different decision makers can be compared through observed choices.     

Anonymity and individual risk

Adverse selection economies with private information are generally studied under the assumption that contracts are exclusive. That is, retrading is prohibited. An alternative market mechanism, the anonymous mechanism, is studied here. Risk averse agents trade contingent claims directly and side markets are in equilibrium. The result is the anonymous equilibrium. The anonymous equilibrium results in a set of endogenous transfers and subsidies.     

First-order risk aversion and non-differentiability

Summary First-order risk aversion happens when the risk premium a decision maker is willing to pay to avoid the lottery , is proportional, for smallt, tot. Equivalently, 0$$ " align="middle" border="0"> . We show that first-order risk aversion is equivalent to a certain non-differentiability of some of the local utility functions (Machina [7]).We are grateful to the Social Sciences and Humanities Research Council of Canada for financial support and to Kim Border, Larry Epstein, Mark Machina and Joe Ostroy for helpful discussions and suggestions.     

The effect of ambiguity aversion on reward scheme choice

We test the implications of ambiguity aversion in a principal–agent problem with multiple agents. Models of ambiguity aversion suggest that, under ambiguity, comparative compensation schemes may become more attractive than independent wage contracts. We test this by presenting agents with a choice between comparative reward schemes and independent contracts, which are designed such that under uncertainty about output distributions (that is, under ambiguity), ambiguity averse agents should typically prefer comparative reward schemes, independent of their degree of risk aversion. We indeed find that the share of agents who choose the comparative scheme is higher under ambiguity.     

Stronger measures of higher-order risk attitudes

This paper aims to extend the results by Ross (1981) [15] and by Modica and Scarsini (2005) [13] to stochastic dominance of degree 4 and over. Specifically, it is shown that Ross' approach can be extended to any order of risk attitude beyond the generalization proposed by Modica and Scarsini by means of sth degree increase in risk defined by Ekern (1980) [8].     

The demand for a risky asset in the presence of a background risk

We examine the demand for a risky asset in the presence of two risks: a financial risk and a background risk which need not be financial. First, we compute the necessary and sufficient condition for a positive demand for a risky asset, showing that it depends on two terms capturing respectively the direct effect of risk premium and the dependence between the two risks. Second, we develop higher order expectation dependence concept and show that the more information about the sign of higher cross derivatives of the utility function we have, the weaker dependence conditions on distribution we achieve.     

First-price sealed-bid auctions when bidders exhibit different attitudes toward risk

When bidders have different risk aversion levels, we determine in a first-price auction, the asymmetric equilibrium strategies. We analyze the impact of asymmetric risk aversion levels on bidders’ markups and on the expected revenue and allocative efficiency of the auction.     

Trading mechanism selection with directed search when buyers are risk averse

We endogenize the trading mechanism selection in a model of directed search with risk averse buyers and show that the unique symmetric equilibrium entails all sellers using fixed price trading. Mechanisms that prescribe the sale price as a function of the realized demand (auctions, bargaining, discount pricing, etc.) expose buyers to the “price risk”, the uncertainty of not knowing how much to pay in advance. Fixed price trading eliminates the price risk, which is why risk averse customers accept paying more to shop at such stores.