Worst-case risk with unspecified risk preferences

20 Pages Posted: 4 Apr 2022

See all articles by Haiyan Liu

Haiyan Liu

Michigan State University - Department of Mathematics

Multiple version iconThere are 2 versions of this paper

Date Written: March 8, 2022

Abstract

In this paper, we study the worst-case distortion risk measure when information about distortion functions is partially available. We obtain the explicit forms of the worst-case distortion functions from several different sets of plausible distortion functions. When there is no concavity constraint on distortion functions, the worst-case distortion function is independent of the risk to be measured and the corresponding worst-case distortion risk measure is a combination of several VaR's at different confidence levels. When the concavity constraint is imposed on distortion functions and the set of concave distortion functions is defined by the riskiness of one single risk, the explicit form of the worst-case distortion function is obtained, which is related to the risk to be measured. When the set of concave distortion functions is defined by the riskiness of multiple risks, we reduce the infinite-dimensional optimization problem to a finite-dimensional optimization problem which can be solved numerically.

Keywords: Value-at-Risk,distortion risk measure, preference robust, concavity[comma separated]

JEL Classification: C02, C61, C44,G32

Suggested Citation

Liu, Haiyan, Worst-case risk with unspecified risk preferences (March 8, 2022). Available at SSRN: https://ssrn.com/abstract=4052907 or http://dx.doi.org/10.2139/ssrn.4052907

Haiyan Liu (Contact Author)

Michigan State University - Department of Mathematics ( email )

619 Red Cedar Road
East Lansing, MI 48824
United States

Do you have a job opening that you would like to promote on SSRN?

Paper statistics

Downloads
59
Abstract Views
231
Rank
532,504
PlumX Metrics