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Quantile-Based Risk Sharing with Heterogeneous Beliefs

Paul Embrechts, Haiyan Liu, Tiantian Mao and Ruodu Wang
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Paul Embrechts: Swiss Federal Institute of Technology Zurich and Swiss Finance Institute
Haiyan Liu: Michigan State University
Tiantian Mao: University of Science and Technology of China (USTC)
Ruodu Wang: University of Waterloo

No 17-65, Swiss Finance Institute Research Paper Series from Swiss Finance Institute

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 (search for similar items in EconPapers)
New Economics Papers: this item is included in nep-gth and nep-rmg
Date: 2017-12, Revised 2018-01
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