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Open AccessArticle

Paradox-Proof Utility Functions for Heavy-Tailed Payoffs: Two Instructive Two-Envelope Problems

Department of Finance, School of Economics and Management, and Schwarzman Scholars Program, Tsinghua University, Beijing 100084, China
Academic Editor: José Garrido
Risks 2015, 3(1), 26-34; https://doi.org/10.3390/risks3010026
Received: 5 October 2014 / Revised: 25 November 2014 / Accepted: 22 December 2014 / Published: 19 January 2015
We identify restrictions on a decision maker’s utility function that are both necessary and sufficient to preserve dominance reasoning in each of two versions of the Two-Envelope Paradox (TEP). For the classical TEP, the utility function must satisfy a certain recurrence inequality. For the St. Petersburg TEP, the utility function must be bounded above asymptotically by a power function, which can be tightened to a constant. By determining the weakest conditions for dominance reasoning to hold, the article settles an open question in the research literature. Remarkably, neither constant-bounded utility nor finite expected utility is necessary for resolving the classical TEP; instead, finite expected utility is both necessary and sufficient for resolving the St. Petersburg TEP. View Full-Text
Keywords: two-envelope paradox; dominance reasoning; von Neumann–Morgenstern utility; heavy-tailed payoffs; boundedness two-envelope paradox; dominance reasoning; von Neumann–Morgenstern utility; heavy-tailed payoffs; boundedness
MDPI and ACS Style

Powers, M.R. Paradox-Proof Utility Functions for Heavy-Tailed Payoffs: Two Instructive Two-Envelope Problems. Risks 2015, 3, 26-34.

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