Optimizing Distortion Riskmetrics With Distributional Uncertainty

46 Pages Posted: 6 Jan 2021 Last revised: 25 Feb 2022

See all articles by Silvana M. Pesenti

Silvana M. Pesenti

University of Toronto

Qiuqi Wang

University of Waterloo - Department of Statistics and Actuarial Science

Ruodu Wang

University of Waterloo - Department of Statistics and Actuarial Science

Date Written: November 11, 2020

Abstract

Optimization of distortion riskmetrics with distributional uncertainty has wide applications in finance and operations research. Distortion riskmetrics include many commonly applied risk measures and deviation measures, which are not necessarily monotone or convex. One of our central findings is a unifying result that allows us to convert an optimization of a non-convex distortion riskmetric with distributional uncertainty to a convex one, leading to great tractability. A sufficient condition to the unifying equivalence result is the novel notion of closedness under concentration, a variation of which is also shown to be necessary for the equivalence. Our results include many special cases that are well studied in the optimization literature, including but not limited to optimizing probabilities, Value-at-Risk, Expected Shortfall, Yaari's dual utility, and differences between distortion risk measures, under various forms of distributional uncertainty. We illustrate our theoretical results via applications to portfolio optimization, optimization under moment constraints, and preference robust optimization.

Keywords: risk measures; deviation measures, distributionally robust optimization, convexification, conditional expectation

JEL Classification: C44, C61,G11

Suggested Citation

Pesenti, Silvana M. and Wang, Qiuqi and Wang, Ruodu, Optimizing Distortion Riskmetrics With Distributional Uncertainty (November 11, 2020). Available at SSRN: https://ssrn.com/abstract=3728638 or http://dx.doi.org/10.2139/ssrn.3728638

Silvana M. Pesenti (Contact Author)

University of Toronto ( email )

100 St. George Street
Toronto, Ontario M5S 3G8
Canada

Qiuqi Wang

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

Waterloo, Ontario N2L 3G1
Canada

Ruodu Wang

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

Waterloo, Ontario N2L 3G1
Canada

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