Characterizing Optimal Allocations in Quantile-Based Risk Sharing
32 Pages Posted: 17 May 2018 Last revised: 3 Jun 2020
Date Written: January 29, 2019
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: Suggested Citation