The optimal payoff for a yaari investor

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Abstract

Yaari's dual theory of choice under risk is the natural counterpart of expected utility theory. While optimal payoff choice for an expected utility maximizer is well studied in the literature, less is known about the optimal payoff for a Yaari investor. We perform a fairly general analysis and derive optimal payoffs in a variety of relevant cases. As a main contribution, we provide the optimal payoff for a Yaari investor under a variance constraint; thus, extending mean–variance optimization to distorted expectation–variance optimization. We also derive the optimal payoff for an investor who aims to outperform an external benchmark under the requirement that the payoff stays in the neighbourhood of this benchmark.
Original languageEnglish
Pages (from-to)1839-1852
Number of pages14
JournalQuantitative Finance
Volume22
Issue number10
DOIs
Publication statusPublished - 28 Jul 2022

Bibliographical note

Funding Information:
This paper was initiated during a research visit of Steven Vanduffel at the University of New South Wales (UNSW) in October 2019. Steven Vanduffel wishes to thank Qihe Tang and all his colleagues for the great hospitality experienced. He also thanks Jaak Moors for his great classes and his encouragement to pursue research. The authors also thank Qihe Tang for the valuable comments received on an earlier version of this draft. They also thank a reviewer for a very careful reading as well as for many useful suggestions and comments that greatly improved the paper.

Publisher Copyright:
© 2022 Informa UK Limited, trading as Taylor & Francis Group.

Copyright:
Copyright 2022 Elsevier B.V., All rights reserved.

Keywords

  • Decision analysis
  • Preferences
  • Cost-efficiency
  • Hoeffding–Fréchet bounds

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