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Quantile-Based Risk Sharing with Heterogeneous Beliefs

Author

Listed:
  • 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)

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.

Suggested Citation

  • Paul Embrechts & Haiyan Liu & Tiantian Mao & Ruodu Wang, 2017. "Quantile-Based Risk Sharing with Heterogeneous Beliefs," Swiss Finance Institute Research Paper Series 17-65, Swiss Finance Institute, revised Jan 2018.
    • Handle: RePEc:chf:rpseri:rp1765
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    Keywords

    Risk Sharing; Competitive Equilibrium; Belief Heterogeneity; Quantiles; Non-Convexity; Risk Measures;
    All these keywords.

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