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Risks 2015, 3(1), 26-34; doi:10.3390/risks3010026

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
Received: 5 October 2014 / Revised: 25 November 2014 / Accepted: 22 December 2014 / Published: 19 January 2015
View Full-Text   |   Download PDF [173 KB, uploaded 19 January 2015]

Abstract

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
This is an open access article distributed under the Creative Commons Attribution License which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited. (CC BY 4.0).

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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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