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Quantile-Based Risk Sharing

Author

Listed:
  • Paul Embrechts

    (Swiss Federal Institute of Technology Zurich and Swiss Finance Institute)

  • Haiyan Liu

    (Michigan State University)

  • Ruodu Wang

    (University of Waterloo)

Abstract

We address the problem of risk sharing among agents using a two-parameter class of quantile-based risk measures, the so-called Range-Value-at-Risk (RVaR), as their preferences. The family of RVaR includes the Value-at-Risk (VaR) and the Expected Shortfall (ES), the two popular and competing regulatory risk measures, as special cases. We first establish an inequality for RVaR-based risk aggregation, showing that RVaR satisfies a special form of subadditivity. Then, the Pareto-optimal risk sharing problem is solved through explicit construction. To study risk sharing in a competitive market, an Arrow-Debreu equilibrium is established for some simple, yet natural settings. Further, we investigate the problem of model uncertainty in risk sharing, and show that, generally, a robust optimal allocation exists if and only if none of the underlying risk measures is a VaR. Practical implications of our main results for risk management and policy makers are discussed, and several novel advantages of ES over VaR from the perspective of a regulator are thereby revealed.

Suggested Citation

  • Paul Embrechts & Haiyan Liu & Ruodu Wang, 2017. "Quantile-Based Risk Sharing," Swiss Finance Institute Research Paper Series 17-54, Swiss Finance Institute.
    • Handle: RePEc:chf:rpseri:rp1754
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    Citations

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    Cited by:

    1. Giovanni Puccetti & Pietro Rigo & Bin Wang & Ruodu Wang, 2019. "Centers of probability measures without the mean," Journal of Theoretical Probability, Springer, vol. 32(3), pages 1482-1501, September.
    2. Mao, Tiantian & Hu, Jiuyun & Liu, Haiyan, 2018. "The average risk sharing problem under risk measure and expected utility theory," Insurance: Mathematics and Economics, Elsevier, vol. 83(C), pages 170-179.
    3. Shengzhong Chen & Niushan Gao & Foivos Xanthos, 2018. "The strong Fatou property of risk measures," Papers 1805.05259, arXiv.org.
    4. Felix-Benedikt Liebrich & Gregor Svindland, 2019. "Risk sharing for capital requirements with multidimensional security markets," Finance and Stochastics, Springer, vol. 23(4), pages 925-973, October.
    5. Felix-Benedikt Liebrich & Gregor Svindland, 2018. "Risk sharing for capital requirements with multidimensional security markets," Papers 1809.10015, arXiv.org.
    6. Weber, Stefan, 2018. "Solvency II, or how to sweep the downside risk under the carpet," Insurance: Mathematics and Economics, Elsevier, vol. 82(C), pages 191-200.

    More about this item

    Keywords

    Value-at-Risk; Expected Shortfall; risk sharing; regulatory capital; robustness; Arrow-Debreu equilibrium;
    All these keywords.

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