Aversion to risk of regret and preference for positively skewed risks
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Aversion to risk of regret and preference for positively skewed risks Christian Gollier1 Received: 31 August 2017 / Accepted: 14 September 2018 © Springer-Verlag GmbH Germany, part of Springer Nature 2018
Abstract We assume that the ex post utility of a regret-sensitive agent facing a menu of lotteries depends upon the payoff of the chosen lottery in the realized state together with the forgone best payoff available in the menu in that state. If two lotteries in the menu have the same distribution of payoffs, the one whose payoff is less statistically concordant with the best alternative yields a larger risk of regret, which should be rejected by regret-risk-averse individuals. This means that regret-risk aversion is equivalent to the supermodularity of the bivariate utility function. We define regret-risk aversion in the small and in the large. We also show that regret-risk aversion tends to induce a bias in favor of the risky act in any one-risky-one-safe menu, in particular when the payoff of the risky choice is highly positively skewed. This is compatible with the “possibility effect” that is well documented in prospect theory. Symmetrically, we define the aversion to rejoicing-risk that can prevail when the ex post utility is alternatively sensitive to the forgone worst payoff. We show that rejoicing-risk-seeking is compatible with the “certainty effect”. We finally show that regret-risk-averse and rejoicing-risk-seeking people behave as if they had rank-dependent utility preferences with an inverse-S shaped probability weighting function that reproduces estimates existing in the literature.
This paper was completed while the author was Wesley Clair Mitchell Visiting Research Professor at the Economics Department of Columbia University, whose hospitality is gratefully acknowledged. I want to thank Mohammed Abdellaoui, Alain Chateauneuf, Keith Crocker, Thomas Epper, Helga Fehr-Duda, Yoram Halevi, Glenn Harrison, Johannes Jaspersen, Thomas Mariotti, Chuck Mason, Pietro Ortoleva, John Quiggin, Klaus Waelde, and Peter Wakker for particularly helpful comments. We also thank seminar participants at the Risk Theory Society meeting, RUD conference, HEC-Paris, Frankfurt workshop in Behavioural Economics, and at CESifo for their comments. The research leading to these results has received funding from the Chairs “Risk Markets and Value Creation” and “Sustainable Finance and Responsible Investments” at TSE.
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Christian Gollier [email protected] Toulouse School of Economics, University of Toulouse-Capitole, 21 Allée de Brienne, 31015 Toulouse Cedex 6, France
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C. Gollier
Keywords Longshot bias · Certainty effect · Possibility effect · Probability weighting · Risk-seeking · Prospect theory · Rejoicing-risk-seeking JEL Classification D81
1 Introduction Regret and rejoicing are emotional reactions to personal past acts. Regret is experienced when realizing that one would have been in a better situation, if only one would have decided differently. Symmetrically, rejoicing is felt when realizing that we
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