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Quantile-Based Risk Sharing

Paul Embrechts, Haiyan Liu and Ruodu Wang
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Paul Embrechts: Swiss Federal Institute of Technology Zurich and Swiss Finance Institute
Haiyan Liu: Michigan State University
Ruodu Wang: University of Waterloo

No 17-54, Swiss Finance Institute Research Paper Series from Swiss Finance Institute

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.

Keywords: Value-at-Risk; Expected Shortfall; risk sharing; regulatory capital; robustness; Arrow-Debreu equilibrium (search for similar items in EconPapers)
New Economics Papers: this item is included in nep-ban and nep-rmg
Date: 2017-12
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