Quantile-based risk sharing

Paul Embrechts (Eidgenössische Technische Hochschule Zürich)

May 3, 2018, 11:00–12:15


Room MC 204

MAD-Stat. Seminar


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. > The results presented are based on joint work with Haiyan Liu and Ruodu Wang, University of Waterloo. > PAPERS: "Quantile-based risk sharing" (2018), Operations Research, to appear, and "Quantile-based risk sharing with heterogeneous beliefs" (2018), submitted.