Characterizing Optimal Allocations in Quantile-Based Risk Sharing

32 Pages Posted: 17 May 2018 Last revised: 3 Jun 2020

See all articles by Ruodu Wang

Ruodu Wang

University of Waterloo - Department of Statistics and Actuarial Science

Yunran Wei

Northern Illinois University; University of Waterloo - Department of Statistics and Actuarial Science

Date Written: January 29, 2019

Abstract

Unlike classic risk sharing problems based on expected utilities or convex risk measures, quantile-based risk sharing games exhibit two special features. First, quantile-based risk measures (such as the Value-at-Risk) are often not convex, and second, they ignore some part of the distribution of the risk. These features create technical challenges in establishing a full characterization of optimal allocations, a question left unanswered in the literature. In this paper, we fully address the issues on the existence and the characterization of optimal allocations in quantile-based risk sharing games. It turns out that negative dependence plays an important role in the optimal allocations, in contrast to positive dependence appearing in classic risk sharing problems. As a by-product of our main finding, we obtain some results on the optimization of the Value-at-Risk and the Expected Shortfall.

Keywords: Risk Sharing, Value-at-Risk, Expected Shortfall, Non-Convexity, Pareto Optimality

JEL Classification: C61, C71

Suggested Citation

Wang, Ruodu and Wei, Yunran, Characterizing Optimal Allocations in Quantile-Based Risk Sharing (January 29, 2019). Insurance: Mathematics and Economics, Forthcoming, Available at SSRN: https://ssrn.com/abstract=3173503 or http://dx.doi.org/10.2139/ssrn.3173503

Ruodu Wang (Contact Author)

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

Waterloo, Ontario N2L 3G1
Canada

Yunran Wei

Northern Illinois University ( email )

1425 W. Lincoln Hwy
Dekalb, IL 60115-2828
United States

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

Waterloo, Ontario N2L 3G1
Canada

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