Dual Utilities on Risk Aggregation under Dependence Uncertainty

Finance and Stochastics, Forthcoming

25 Pages Posted: 30 Nov 2017 Last revised: 30 Jun 2019

See all articles by Ruodu Wang

Ruodu Wang

University of Waterloo - Department of Statistics and Actuarial Science

Zuo Quan Xu

Hong Kong Polytechnic University

Xun Yu Zhou

Columbia University - Department of Industrial Engineering and Operations Research (IEOR)

Date Written: November 26, 2017

Abstract

Finding the worst-case value of a preference over a set of plausible models is a well-established approach to address the issue of model uncertainty or ambiguity. In this paper, we study the worst-case evaluation of Yaari’s dual utility functionals of an aggregate risk under dependence uncertainty along with its decision-theoretic implications. To arrive at our main findings, we introduce a technical notion of conditional joint mixability. Lower and upper bounds on dual utilities with dependence uncertainty are established and, in the presence of conditional joint mixability, they are shown to be exact bounds. A particular economic implication of our results is what we call the pessimism effect. We show that a (generally non-convex/nonconcave) dual utility-based decision maker under dependence uncertainty behaves as if she had a more pessimistic risk-averse dual utility but free of dependence uncertainty.

Keywords: Dual Utility; Conditional Joint Mixability; Risk Aggregation; Dependence Uncertainty; Pessimism Effect

Suggested Citation

Wang, Ruodu and Xu, Zuo Quan and Zhou, Xunyu, Dual Utilities on Risk Aggregation under Dependence Uncertainty (November 26, 2017). Finance and Stochastics, Forthcoming, Available at SSRN: https://ssrn.com/abstract=3078374 or http://dx.doi.org/10.2139/ssrn.3078374

Ruodu Wang (Contact Author)

University of Waterloo - Department of Statistics and Actuarial Science ( email )

Waterloo, Ontario N2L 3G1
Canada

Zuo Quan Xu

Hong Kong Polytechnic University ( email )

Hung Hom
Kowloon, 0
Hong Kong

Xunyu Zhou

Columbia University - Department of Industrial Engineering and Operations Research (IEOR) ( email )

331 S.W. Mudd Building
500 West 120th Street
New York, NY 10027
United States

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