Characterizing optimal allocations in quantile-based risk sharing

Author ORCID Identifier

Yunran Wei:https://orcid.org/0000-0002-9616-9454

Publication Title

Insurance: Mathematics and Economics

ISSN

01676687

E-ISSN

44013

Document Type

Article

Abstract

Unlike classic risk sharing problems based on expected utilities or convex risk measures, quantile-based risk sharing problems 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 address the issues on the existence and the characterization of (Pareto-)optimal allocations in risk sharing problems for the Range-Value-at-Risk family. It turns out that negative dependence, mutual exclusivity in particular, 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 (VaR) and the Expected Shortfall, as well as a new result on the inf-convolution of VaR and a general distortion risk measure.

First Page

288

Last Page

300

Publication Date

7-1-2020

DOI

10.1016/j.insmatheco.2020.06.001

Keywords

Expected Shortfall, Non-convexity, Pareto optimality, Risk sharing, Value-at-Risk

Department

Department of Statistics and Actuarial Science

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