41 Pages Posted: 10 Mar 2016 Last revised: 8 Mar 2017
Date Written: March 5, 2017
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
JEL Classification: G10, O16
Suggested Citation: Suggested Citation
Embrechts, Paul and Liu, Haiyan and Wang, Ruodu, Quantile-Based Risk Sharing (March 5, 2017). Available at SSRN: https://ssrn.com/abstract=2744142