Sharing the Value-at-Risk Under Distributional Ambiguity

29 Pages Posted: 17 Jun 2019 Last revised: 2 Dec 2020

See all articles by Zhi Chen

Zhi Chen

Department of Decisions, Operations and Technology, CUHK Business School, The Chinese University of Hong Kong

Weijun Xie

Georgia Institute of Technology

Date Written: June 6, 2019

Abstract

This paper considers the problem of risk sharing, where a coalition of homogeneous agents, each bearing a random cost, aggregates their costs and shares the value-at-risk of such a risky position. Due to limited distributional information in practice, the joint distribution of agents' random costs is difficult to acquire. The coalition, being aware of the distributional ambiguity, thus evaluates the worst-case value-at-risk within a commonly agreed ambiguity set of the possible joint distributions. Through the lens of cooperative game theory, we show that this coalitional worst-case value-at-risk is subadditive for the popular ambiguity sets in the distributionally robust optimization literature that are based on (i) convex moments or (ii) Wasserstein distance to some reference distributions. In addition, we propose easy-to-compute core allocation schemes to share the worst-case value-at-risk. Our results can be readily extended to sharing the worst-case conditional value-at-risk under distributional ambiguity.

Keywords: Risk sharing, value-at-risk, conditional value-at-risk, distributionally robust optimization

Suggested Citation

Chen, Zhi and Xie, Weijun, Sharing the Value-at-Risk Under Distributional Ambiguity (June 6, 2019). Available at SSRN: https://ssrn.com/abstract=3400033 or http://dx.doi.org/10.2139/ssrn.3400033

Zhi Chen (Contact Author)

Department of Decisions, Operations and Technology, CUHK Business School, The Chinese University of Hong Kong ( email )

Room 952, 9/F, Cheng Yu Tong Building
The Chinese University of Hong Kong, Shatin.
Hong Kong
Hong Kong

Weijun Xie

Georgia Institute of Technology ( email )

Atlanta, GA 30332
United States

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

Paper statistics

Downloads
235
Abstract Views
1,285
Rank
268,417
PlumX Metrics