Allais, Ellsberg, and preferences for hedging

Allais, Ellsberg, and Preferences for Hedging

Generalized Optimized Certainty Equivalent with Applications in the Rank-dependent Utility Model

In this chapter a new model of choice under risk within the framework of RDU theory is offered. The suggested model contains the expected utility model as a special case. Compared to anticipated utility theory it is more general in one respect and more restrictive in another. It is more general since it allows the probability distortion to depend on the prizes available. But it restricts on the other hand these distortions to be homogeneous in the probabilities.

Expected utility theory and inner and outer measures of loss aversion

While economists in the past tended to assume that individual preferences, including risk preferences, are stable over time, a recent literature has developed and indicates that risk preferences respond to shocks, with mixed evidence on the direction of the responses. This paper utilizes a natural experiment with covariate (drought) and idiosyncratic shocks in combination with an independent field risk experiment. The risk experiment uses a Certainty Equivalent-Multiple Choice List approach and is played 1–2 years after the subjects were (to a varying degree) exposed to a covariate drought shock or idiosyncratic shocks for a sample of resource-poor young adults living in a risky semi-arid rural environment in Sub-Saharan Africa. The experimental approach facilitates a comprehensive assessment of shock effects on experimental risk premiums for risky prospects with varying probabilities of good and bad outcomes. The experiment also facilitates the estimation of the utility curvature in an Expected Utility (EU) model and, alternatively, separate estimation of probability weighting and utility curvature in three different Rank Dependent Utility models with a two-parameter Prelec probability weighting function. Our study is the first to comprehensively test the theoretical predictions of Gollier and Pratt (Econom J Econom Soc 64:1109–1123, 1996) versus Quiggin (Econ Theor 22(3):607–611, 2003). Gollier and Pratt (1996) build on EU theory and state that an increase in background risk will make subjects more risk averse while Quiggin (2003) states that an increase in background risk can enhance risk-taking in certain types of non-EU models. We find strong evidence that such non-EU preferences dominate in our sample.

Victor prefers safety more than Ursula if whenever Ursula prefers a constant to an uncertain act, so does Victor. This paradigm, whose expected utility (EU) version is Arrow and Pratt’s more risk aversion concept, will be studied in the Choquet expected utility (CEU) model. Necessary condition Pointwise inequality between a function of the utility functions and another of the capacities is necessary and sufficient for the preference by Victor of safety over a dichotomous act whenever such is the preference of Ursula. However, increased preference for safety versus dichotomous acts does not imply preference by Victor of safety over a general act whenever such is the preference of Ursula. A counterexample will be provided, via the casino theory of Dubins and Savage. Sufficient condition Separation of the two functions by some convex function is sufficient for Victor to prefer safety more than Ursula, over general acts. Furthermore, a condition on the capacities will be presented for simplicity seeking, the preference by Victor over any act for some dichotomous act that leaves Ursula indifferent. This condition is met in particular if Victor’s capacity is a convex function of Ursula’s capacity. For these cases, the pointwise inequality (necessary) condition is a characterization of greater preference for safety, extending the Arrow–Pratt notion from EU to CEU and rank-dependent utility (RDU). These inequalities preserve the flavor of the “more pessimism than greediness” characterization of monotone risk aversion by Chateauneuf, Cohen and Meilijson in the RDU model and its extension by Grant and Quiggin to CEU. Preferences between safety and dichotomous acts are at the core of the biseparable preferences model of Ghirardato and Marinacci.

We introduce a model of random ambiguity aversion. Choice is stochastic due to unobserved shocks to both information and ambiguity aversion. This is modeled as a random set of beliefs in the maxmin expected utility model of Gilboa and Schmeidler (1989). We characterize the model and show that the distribution of ambiguity aversion can be uniquely identified from binary choices. A novel stochastic order on random sets is introduced that characterizes greater uncertainty aversion under stochastic choice. If the set of priors is the Aumann expectation of the random set, then choices satisfy dynamic consistency. This corresponds to an agent who knows the distribution of signals but is uncertain about how to interpret signal realizations. More broadly, the analysis of stochastic properties of random ambiguity attitudes provides a theoretical foundation for the study of other random nonlinear utility models.

Attitude towards risk is important to individual decision making. Rank-dependent utility theory is an appealing framework within which to study decision making under risk. This paper specifies Rank-Dependent Utility (RDU) models in the context of a stated choice experiment of commuter's risky route choice to (a) estimate willingness to pay for travel time, and (b) understand the risk attitudes of sampled respondents and their socioeconomic characteristics. We also allow for unobserved taste heterogeneity within an RDU framework using a mixed multinomial logit model. The findings provide a new set of empirical estimates of the value of travel time savings that allow for travel time variability combined into a single measure, referred to as the value of expected travel time savings.

Stiglitz (1977) established three well-known features of monopoly insurance markets subject to adverse selection: (i) at least one market segment is served, despite the informational asymmetry; (ii) there is always some screening of risk classes; and (iii) efficiency is sacrificed to achieve screening. We modify Stiglitz’s model, replacing his expected utility assumption on consumer behavior with a version of Quiggin’s (1982) rank-dependent utility model that has received strong experimental support. We show that none of the conclusions (i)—(iii) is robust to this revision. In particular, asymmetric information need not lead to any loss in efficiency.

We develop a revealed preference test for the Choquet expected utility model with ambiguity aversion, which does not rely on specific functional form assumptions on the utility index. It is computationally efficient if the number of states is not too large, even for a large number of observations. This is a nice feature compared to other existing revealed preference tests for decision models with ambiguity. We illustrate the usefulness of our results by implementing our test on two experimental datasets from the literature, and we compare the empirical fit of this model to the subjective expected utility model. (JEL C91, D81, D91, G41)

The dominant theory of individual decision making under uncertainty is the von Neumann and Morgenstern's expected utility model (EUM). Although, this model has gained its popularity from its ability to explain a wide range of attitudes toward risk, empirical evidence over the last three decades has documented paradoxical behavior that is inconsistent with the EUM model. The present study examines in an experimental setting individuals' inconsistent behavior in choosing between two pairs of lotteries known as the Allais paradox. This study extends previous literature on money gamble situations by conducting a series of experiments to test expected utility behavior on auditing student subjects in pure money and audit settings. Two variants of audit settings are examined: overall audit plan case and audit procedure evaluation of internal control case.

Experimental tests of expected-utility theory (EU) have accumulated empirical observations in which the predictions of EU are systematically violated. The cumulative prospect theory (CPT) explains violations such as the Allais paradoxes and fourfold pattern of risk attitudes as resulting from nonlinear probability transformations. Here we show that the classical paradoxes for decisions under risk can be explained with preferences that are linear in probabilities for any choice set and that maximize an expected-utility function with respect to an endogenous target return. We introduce the maximin payoff as a plausible and even natural target return from a choice set and show that the resulting target-adjusted utility (TAU) model explains additional empirical observations such as the scale dependence of the Allais paradox that cannot be explained by standard specifications of CPT. Further, using data from three prominent laboratory experiments, we find that TAU is effective in explaining observed behaviors. This paper was accepted by James Smith, decision analysis.

Subjective uncertainty is characterized by ambiguity if the decision maker has an imprecise knowledge of the probabilities of payoff relevant events. In such an instance, the decision maker's beliefs are better represented by a set of probability functions than by a unique probability function. An ambiguity averse decision maker adjusts his choice on the side of caution in response to his imprecise knowledge of the odds. The non-additive expected utility model allows a formal characterization of such behavior. Using this model, this paper shows that ambiguity aversion can explain the existence of incomplete contracts. The setting for the demonstration is the investment hold-up model which has been the focus of much of the recent research on the implications of incomplete contracts.

Maxmin expected utility in Savage's framework

Expected Utility and Sequential Elimination Models of Career Decision Making