Decision making under risk in Deal or No Deal

We analyse the choices of 399 contestants in the Australian version of the television game show Deal or No Deal. We calculate risk aversion bounds for each contestant, revealing considerable heterogeneity. We then estimate a structural stochastic choice model that captures the dynamic decision problem faced by contestants. To address individual heterogeneity, we nest the dynamic problem within the settings of both a random effects and a random coefficients probit model. Our structural model produces plausible estimates of risk aversion, confirms the role of individual heterogeneity and suggests that a model of stochastic choice is indeed appropriate. We find mixed evidence of greater risk aversion by females. We also examine generalizations to expected utility theory, finding that the rank‐dependent utility model adds non‐negligible explanatory power and indicates optimism in probability weighting. Finally, we test, but are unable to confirm, the existence of an endowment effect for lotteries. Copyright © 2009 John Wiley & Sons, Ltd.     

Risk aversion in Entrepreneurship Panels: Measurement Problems and Alternative Explanations

In this study, we investigate the pitfalls associated with measuring risk aversion within studies of entrepreneurial behavior. First, we raise substantial concerns as to whether standard questions employed can be used to infer risk aversion among nascent entrepreneurs. In our work we show that the US, Canadian and Swedish panel study datasets do not offer evidence that entrepreneurs are more risk averse than non‐entrepreneurs. In fact, we show that the measurements used for risk aversion in these studies are not compatible with classic expected utility theory. Furthermore, our analysis reveals that probability weighting may even counteract the respondent's risk attitude. Therefore, inferring the respondent's risk attitude from choices in the panel study datasets can be misleading in the presence of probability weighting. We therefore suggest that alternative theories of decision making under risk, like prospect theory, are relevant and should be taken into account in future studies on entrepreneurship. Copyright © 2017 John Wiley & Sons, Ltd.     

Are CEOs expected utility maximizers?

Are individuals expected utility maximizers? This question represents much more than academic curiosity. In a normative sense, at stake are the fundamental underpinnings of the bulk of the last half-century’s models of choice under uncertainty. From a positive perspective, the ubiquitous use of benefit-cost analysis across government agencies renders the expected utility maximization paradigm literally the only game in town. In this study, we advance the literature by exploring CEO’s preferences over small probability, high loss lotteries. Using undergraduate students as our experimental control group, we find that both our CEO and student subject pools exhibit frequent and large departures from expected utility theory. In addition, as the extreme payoffs become more likely CEOs exhibit greater aversion to risk. Our results suggest that use of the expected utility paradigm in decision making substantially underestimates society’s willingness to pay to reduce risk in small probability, high loss events.     

Discrete-time behavioral portfolio selection under cumulative prospect theory

We formulate and study three multi-period behavioral portfolio selection models under cumulative prospect theory: (i) S-shaped utility maximization without probability weighting in a market with one risky asset; (ii) S-shaped utility maximization without probability weighting in a market with multiple risky assets which follow a joint elliptical distribution; and (iii) S-shaped utility maximization with inverse-S-shaped probability weighting in a market with one risky asset. For the first two time consistent models, we identify the well-posedness conditions and derive the semi-analytical optimal policies. For the third time inconsistent model, we assume that the investor is aware of the time inconsistency but is unable to commit to his initial plan of action. Then, we reformulate the model into an intrapersonal game model and derive the semi-analytical subgame perfect Nash equilibrium (time consistent) policy under well-posedness condition. All the three policies take a piecewise linear feedback form. Our analysis of the three models not only partially explains the well documented phenomena of non-participation puzzle and horizon effect, but also extends the two fund separation theorem into multi-period S-shaped utility setting and pushes forward the study on time inconsistency issue incurred by probability weighting.     

Rationalizing investors’ choices

Assuming that agents’ preferences satisfy first-order stochastic dominance, we show how the Expected Utility paradigm can rationalize all optimal investment choices: the optimal investment strategy in any behavioral law-invariant (state-independent) setting corresponds to the optimum for an expected utility maximizer with an explicitly derived concave non-decreasing utility function. This result enables us to infer the utility and risk aversion of agents from their investment choice in a non-parametric way. We relate the property of decreasing absolute risk aversion (DARA) to distributional properties of the terminal wealth and of the financial market. Specifically, we show that DARA is equivalent to a demand for a terminal wealth that has more spread than the opposite of the log pricing kernel at the investment horizon.     

A simple mean–dispersion model of ambiguity attitudes

Several characterizations of ambiguity aversion decompose preferences into the expected utility of an act and an adjustment factor, an ambiguity index, or a dispersion function. In each of these cases, the adjustment factor has very little structure imposed on it, and thus these models provide little guidance as to which function to use from the infinite class of possible alternatives. In this paper, we provide a simple axiomatic characterization of mean–dispersion preferences which uniquely determines a subjective probability distribution over a set of possible priors and which uniquely identifies the dispersion function. We provide an algorithm for determining this subjective probability distribution and the coefficient in the dispersion function from experimental data. We also demonstrate that the model accommodates ambiguity aversion in the Ellsberg paradox.     

Is insurance normal or inferior? -A regret theoretical approach-

This study considers how changes in wealth affect insurance demand when individuals suffer disutility from regret. Anticipated regret stems from a comparison between the ex-post maximum and actual wealth. We consider a situation wherein individuals maximize their expected utility incorporating anticipated regret. The wealth effect on insurance demand can be classified into the risk and the regret effects. These effects are determined by the properties of the utility function and the regret function. We show that insurance can be normal when individuals place weight on anticipated regret, even though the utility function exhibit decreasing absolute risk aversion. This result indicates that regret theory is a possible explanation to the wealth effect puzzle, in which insurance is normal from empirical observation, but it should be inferior by theoretical prediction under expected utility theory.     

Diversification preferences in the theory of choice

Diversification represents the idea of choosing variety over uniformity. Within the theory of choice, desirability of diversification is axiomatized as preference for a convex combination of choices that are equivalently ranked. This corresponds to the notion of risk aversion when one assumes the von Neumann–Morgenstern expected utility model, but the equivalence fails to hold in other models. This paper analyzes axiomatizations of the concept of diversification and their relationship to the related notions of risk aversion and convex preferences within different choice theoretic models. Implications of these notions on portfolio choice are discussed. We cover model-independent diversification preferences, preferences within models of choice under risk, including expected utility theory and the more general rank-dependent expected utility theory, as well as models of choice under uncertainty axiomatized via Choquet expected utility theory. Remarks on interpretations of diversification preferences within models of behavioral choice are given in the conclusion.     

基于心理账户和后悔理论的报童问题研究

考虑到零售商存货后悔和缺货后悔的心理效用,文章将心理账户理论和后悔理论纳入报童模型,建立了报童的随机后悔效用函数,证明了期望后悔效用函数的凹性,以及最优购量满足的最优性条件。同时解析地进行了存货后悔和缺货后悔决策权重系数的比较静态分析。结果发现:其最优订购量随存货后悔权重系数增加而减少,随缺货后悔权重系数增加而增加。最后,数值验证了存货后悔和缺货后悔对最优订购量的影响。     

Risk aversion for variational and multiple-prior preferences

The objective of this paper is to identify variational preferences and multiple-prior (maxmin) expected utility functions that exhibit aversion to risk under some probability measure from among the priors. Risk aversion has profound implications on agents’ choices and on market prices and allocations. Our approach to risk aversion relies on the theory of mean-independent risk of Werner (2009). We identify necessary and sufficient conditions for risk aversion of convex variational preferences and concave multiple-prior expected utilities. The conditions are stability of the cost function and of the set of probability priors, respectively, with respect to a probability measure. The two stability properties are new concepts. We show that cost functions defined by the relative entropy distance or other divergence distances have that property. Set of priors defined as cores of convex distortions of probability measures or neighborhoods in divergence distances have that property, too.     

When Ross meets Bell: The linex utility function

At first glance, there would appear to be no relationship between Bell’s (1988) concept of one-switch utility functions and that of a stronger measure of risk aversion due to Ross (1981). We show however that specific assumptions about the behavior of the stronger measure of risk aversion also give rise to the linex utility function which belongs to the class of one-switch utility functions. In particular, this utility class is the only one that satisfies a stronger version of Kimball’s (1993) standard risk aversion over all levels of wealth. We apply our results to consider n$n$th-degree deteriorations in background risk and their effect on risk taking behavior.     

An examination of linear factor models in country equity asset allocation strategies

We examine the out of sample performance of country equity asset allocation strategies between January 1985 and February 2000 that use conditional versions of international asset pricing models to forecast expected returns. We find that strategies that use conditional asset pricing models tend not to outperform a strategy that uses the sample mean to forecast expected returns. We find that this result is fairly robust across different levels of risk aversion, whether riskless lending is available or not, and when we impose upper bound constraints.     

Accounting for optimism and pessimism in expected utility

We provide a preference foundation for decision under risk resulting in a model where probability weighting is linear as long as the corresponding probabilities are not extreme (i.e., 0 or 1). This way, most of the elegance and mathematical tractability of expected utility is maintained and also much of its normative foundation. Yet, the new model can accommodate the extreme sensitivity towards changes from 0 to almost impossible and from almost certain to 1 that has widely been documented in the experimental literature. The model can be viewed as “expected utility with the best and worst in mind” as suggested by Chateauneuf, Eichberger and Grant (Chateauneuf, Alain, Eichberger, Jürgen, Grant, Simon, 2007. Choice under uncertainty with the best and worst in mind: NEO-Additive capacities. Journal of Economic Theory 137, 538–567) or, following our preference foundation, interpreted as “expected utility with consistent optimism and pessimism”.     

Optimal investment for executive stockholders with exponential utility

The scope of this paper is to enhance the model for the own-company stockholder (Desmettre et?al. in Math Methods Oper Res 72(3):347?C378, 2010), who can voluntarily performance-link his personal wealth to his management success by acquiring stocks in the own-company whose value he can directly influence via spending work effort. The executive is thereby characterized by a parameter of risk aversion and the two work effectiveness parameters inverse work productivity and disutility stress. We extend the model to a constant absolute risk aversion framework using an exponential utility/disutility setup. A closed-form solution is given for the optimal work effort an executive will apply and we derive the optimal investment strategies of the executive. Furthermore, we determine an up-front fair cash compensation applying an indifference utility rationale. Our study shows to a large extent that the results previously obtained are robust under the choice of the utility/disutility setup.     

Linear cumulative prospect theory with applications to portfolio selection and insurance demand

Abstract The present paper combines loss attitudes and linear utility by providing an axiomatic analysis of corresponding preferences in a cumulative prospect theory (CPT) framework. In a sense we derive a two-sided variant of Yaari’s dual theory, i.e., nonlinear probability weights in the presence of linear utility. The first important difference is that utility may have a kink at the status quo, which allows for the exhibition of loss aversion. Also, we may have different probability weighting functions for gains than for losses. We apply the model to both portfolio selection and insurance demand. Our results show that CPT with linear utility has more realistic implications than the dual theory since it implies only a weakened variant of plunging. Mathematics Subject Classification (2000): 91B08, 91B28, 91B30 Journal of Economic Literature Classification: D81, G11, G22     

Equilibrium asset pricing with Epstein-Zin and loss-averse investors

We study multi-period equilibrium asset pricing in an economy with Epstein-Zin (EZ-) agents whose preferences for consumption are represented by recursive utility and with loss averse (LA-) agents who derive additional utility of gains and losses and are averse to losses. We propose an equilibrium gain-loss ratio for stocks and show that the LA-agents are more (less) risk averse than the EZ-agents if their degree of loss aversion is higher (lower) than this ratio. When all the agents have unitary relative risk aversion degree and elasticity of intertemporal substitution, we prove the existence and uniqueness of the equilibrium and the market dominance of the EZ-agents in the long run. Finally, we extend our results to the case in which the LA-agents use probability weighting in their evaluation of gains and losses.     

Disappointment aversion in tournaments

Many experiments and field studies indicate that individuals have an asymmetric attitude towards gains versus losses. In this paper, we extend the canonic tournament model by assuming the workers' preferences exhibit disappointment aversion. First, we find the winning prize is first increasing and then decreasing in volatility and the losing prize shows the opposite. Furthermore, when the volatility exceeds a threshold, both the winning and losing prizes are reduced to zero. By contrast, there is no such kink for the risk aversion case. Finally, we find the piece rates always dominate rank-order tournaments when the workers are disappointment averse.     

Multivariate risk aversion utility,application to ESG investments

This paper uses the concept of multivariate or multi-attributive utility to attach different risk aversion levels to different sources of wealth (e.g. sectors, stocks, asset classes). In this context, we address the topic of environmental, social, and corporate governance (ESG) investments from the perspective of an investor with different risk aversion levels to green and brown stocks. We obtain closed-form solutions for the optimal allocations, value function, and wealth equivalent losses (WEL) from suboptimal choices. The numerical analysis demonstrates the significant increase, of up to 33%, in green investments when accounting for a differential in risk aversions levels, with up to 65% in WEL when using same risk-aversion levels.¹     

Decision making with imprecise probabilistic information

We develop an axiomatic approach to decision under uncertainty that explicitly takes into account the information available to the decision maker. The information is described by a set of priors and a reference prior. We define a notion of imprecision for this informational setting and show that a decision maker who is averse to information imprecision maximizes the minimum expected utility computed with respect to a subset of the set of initially given priors. The extent to which this set is reduced can be seen as a measure of imprecision aversion. This approach thus allows a lot of flexibility in modelling the decision maker attitude towards imprecision. In contrast, applying Gilboa and Schmeidler [J. Math. Econ. 18 (1989) 141] maxmin criterion to the initial set of priors amounts to assuming extreme pessimism.     

Problem-solving effort and success in innovation contests: The role of national wealth and national culture

Innovation contests allow firms to harness specialized skills and services from globally dispersed participants for solutions to business problems. Such contests provide a rich setting for operations management (OM) scholars to explore problem solving in global labor markets as firms continue to unbundle their innovation value chains. In this study, we examine the implications of specific types of diversity in innovation contests on problem-solving effort and success. First, we conceptualize diversity among contestants in terms of national wealth (measured as gross domestic product per capita (GDPP) adjusted for purchasing power parity) and national culture (measured using the culture dimensions of performance orientation and uncertainty avoidance) and examine how such factors influence problem-solving effort. Next, we examine how differences between contestants and contest holders in terms of the above factors influence contest outcomes. Using data from a popular online innovation contest platform and country-level archival data, we find that contestants from countries with lower levels of GDPP are more likely to exert greater problem-solving effort compared to other contestants. With regard to national culture, we find that performance orientation and uncertainty avoidance have positive and negative effects, respectively, each of which weakens with increasing levels of GDPP. Finally, our analysis provides evidence of homophily effects indicating that contestants who share greater similarities with the contest holder in terms of national wealth and national culture are more likely to be successful in a contest. We discuss the implications of the study's findings for contest holders and platform owners who organize innovation contests, and for emerging research on innovation contests.