Quantile-Based Risk Sharing with Heterogeneous Beliefs

30 Pages Posted: 6 Dec 2017 Last revised: 17 Jul 2018

See all articles by Paul Embrechts

Paul Embrechts

Swiss Federal Institute of Technology Zurich; Swiss Finance Institute

Haiyan Liu

Michigan State University - Department of Mathematics

Tiantian Mao

University of Science and Technology of China (USTC) - Department of Statistics and Finance

Ruodu Wang

University of Waterloo - Department of Statistics and Actuarial Science

Date Written: November 29, 2017

Abstract

We study risk sharing games with quantile-based risk measures and heterogeneous beliefs, motivated by the use of internal models in finance and insurance. Explicit forms of Pareto-optimal allocations and competitive equilibria are obtained by solving various optimization problems. For Expected Shortfall (ES) agents, Pareto-optimal allocations are shown to be equivalent to equilibrium allocations, and the equilibrium price is unique. For Value-at-Risk (VaR) agents or mixed VaR and ES agents, a competitive equilibrium does not exist. Our results generalize existing ones on risk sharing games with risk measures and belief homogeneity, and draw an interesting connection to early work on optimization properties of ES and VaR.

Keywords: Risk Sharing, Competitive Equilibrium, Belief Heterogeneity, Quantiles, Non-Convexity, Risk Measures

Suggested Citation

Embrechts, Paul and Liu, Haiyan and Mao, Tiantian and Wang, Ruodu, Quantile-Based Risk Sharing with Heterogeneous Beliefs (November 29, 2017). Swiss Finance Institute Research Paper No. 17-65, Available at SSRN: https://ssrn.com/abstract=3079998 or http://dx.doi.org/10.2139/ssrn.3079998

Paul Embrechts

Swiss Federal Institute of Technology Zurich ( email )

ETH-Zentrum
CH-8092 Zurich
Switzerland

Swiss Finance Institute

c/o University of Geneva
40, Bd du Pont-d'Arve
CH-1211 Geneva 4
Switzerland

Haiyan Liu

Michigan State University - Department of Mathematics ( email )

619 Red Cedar Road
East Lansing, MI 48824
United States

Tiantian Mao

University of Science and Technology of China (USTC) - Department of Statistics and Finance ( email )

96, Jinzhai Road
Hefei, Anhui 230026
China

Ruodu Wang (Contact Author)

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

Waterloo, Ontario N2L 3G1
Canada

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