Developments in Non-Expected Utility Theories: An Empirical Study of Risk Aversion

By Aissia, Dorsaf Ben | Journal of Economics and Finance, April 2016 | Go to article overview

Developments in Non-Expected Utility Theories: An Empirical Study of Risk Aversion


Aissia, Dorsaf Ben, Journal of Economics and Finance


(ProQuest: ... denotes formulae omitted.)

1 Introduction

Recent financial literature highlights the relevance of the non-expected utility theory in explaining agents' behavior towards monetary gambles (Epstein and Zin 1990; Rabin 2000; Barberis and Huang 2006; Barberis et al. 2006). This literature reveals that the expected utility model fails to describe the small stakes gambles,1 as it provides for significant risk aversion, leading to the rejection of another type of gamble, namely the large2 stakes gamble.

A first area of research related to our work groups studies of non-expected utility. Different value functions and weighted probability functions were proposed in the literature. However, relevant behavioral finance literature outlines the prevalence of Prospect Theory3 of Kahneman and Tversky (1979)(Starmer2000;Postetal.2008; Chou et al. 2009). For instance, Starmer (2000)examinesasetofnon-expectedutility theories and concludes that Prospect Theory constitutes a well grounded hypothesis departing from the standard theory of expected utility. Post et al. (2008)documentthat the loss-aversion value function proposed in Prospect Theory explains the agents' choices substantially better than the expected utility does. Chou et al. (2009)confirm this finding and show strong and robust evidence supporting Prospect Theory.

A second area of behavioral finance literature focuses on non-deterministic approaches of choice under risk and uncertainty that address expected utility violations. These approaches are commonly grouped under the name of random utility maximization models. 4 Harless and Camerer (1994), Hey and Orme (1994) and Loomes and Sugden (1995) present the first studies integrating a stochastic specification in utility models. For instance, Hey and Orme (1994)findthatanexpectedutility, with some additional structure of error terms, provides satisfactory predictions of individual choice. Recently, de Palma et al. (2008) highlighted the cross-fertilizations of random utility models with the study of decision making under risk and uncertainty, and recommended researchers to estimate people's preferences based on the specification of a random utility model.

Finally, a growing number of studies use real monetary gambles provided by TV game shows to examine investors' risky choices. Among the studied games, we cite Card Sharks (Gertner 1993), Jeopardy! (Metric 1995), Illinois Instant Riches (Hersch and McDougall 1997), Lingo (Beetsman and Schotman 2001), Hoosier Millionaire (Fullencamp et al. 2003), Who Wants to be a Millionaire? (Hartley et al. 2005) and Deal or No Deal (Post et al. 2006; Roos and Sarafidis 2006;Postetal.2008; Van Den Assem 2008). The relevance of these studies is to provide estimates of the agents' risk aversion based on real data of monetary gambles.

This paper investigates different developments in non-expected utility theories using the case of the Deal or No Deal game show. Our results complement thoseofPostetal.(2008) in two respects. First, we integrate non-linear probability weighting functions into the loss-aversion value function of Prospect Theory. Post et al. (2008) focus specifically on utility models which have a smooth probability weighting function. However, this study examines the rank-dependant utility model and the Cumulative Prospect Theory of Tversky and Kahneman (1992). Introducing different shapes of the probability weighting function improves the robustness of our results since it detects the investor's sentiment of optimism (pessimism) that is not necessarily captured by the value functions. Second, our behavioral specifications are defined in a random utility model framework since we integrate a noise term into the contestants' preferences, as in Hey and Orme (1994). In fact, the very reason for the interest in the random utility model is that the noise term could reflect errors in the contestants' decisions that are not identified in the standard utility models. …

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