Baccelli, Jean and Schollmeyer, Georg and Jansen, Christoph (2021) Risk Aversion over Finite Domains. Theory and Decision.

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Abstract

We investigate risk attitudes when the underlying domain of payoffs is finite and the payoffs are, in general, not numerical. In such cases, the traditional notions of absolute risk attitudes, that are designed for convex domains of numerical payoffs, are not applicable. We introduce comparative notions of weak and strong risk attitudes that remain applicable. We examine how they are characterized within the rank-dependent utility model, thus including expected utility as a special case. In particular, we characterize strong comparative risk aversion under rank-dependent utility. This is our main result. From this and other findings, we draw two novel conclusions. First, under expected utility, weak and strong comparative risk aversion are characterized by the same condition over finite domains. By contrast, such is not the case under non-expected utility. Second, under expected utility, weak (respectively: strong) comparative risk aversion is characterized by the same condition when the utility functions have finite range and when they have convex range (alternatively, when the payoffs are numerical and their domain is finite or convex, respectively). By contrast, such is not the case under non-expected utility. Thus, considering comparative risk aversion over finite domains leads to a better understanding of the
divide between expected and non-expected utility, more generally, the structural properties of the main models of decision-making under risk.

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Item Type:	Published Article or Volume
Creators:	Creators Email ORCID Baccelli, Jean jean.baccelli@gmail.com 0000-0003-0275-0377 Schollmeyer, Georg Jansen, Christoph
Keywords:	risk aversion; comparative risk aversion; expected utility; non-expected utility; rank-dependent utility; dual expected utility
Subjects:	General Issues > Decision Theory Specific Sciences > Economics General Issues > Game Theory Specific Sciences > Psychology > Judgment and Decision Making Specific Sciences > Probability/Statistics
Depositing User:	Jean Baccelli
Date Deposited:	06 Nov 2021 18:53
Last Modified:	06 Nov 2021 18:53
Item ID:	19813
Journal or Publication Title:	Theory and Decision
Publisher:	Springer
DOI or Unique Handle:	10.1007/s11238-021-09847-8
Subjects:	General Issues > Decision Theory Specific Sciences > Economics General Issues > Game Theory Specific Sciences > Psychology > Judgment and Decision Making Specific Sciences > Probability/Statistics
Date:	2021
URI:	https://philsci-archive.pitt.edu/id/eprint/19813

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