Quantile-based risk sharing, market equilibria, and belief heterogeneity

Ruodu Wang
University of Waterloo

Wednesday, Nov 14, 2018
4:15 - 5:15 PM
Location: Huang 305


We establish a general framework of risk sharing games for agents using quantile-based risk measures as their preferences. The family of quantile-based risk measures includes the Value-at-Risk (VaR) and the Expected Shortfall (ES), the two popular and competing regulatory risk measures, as special cases. Motivated by the extensive use of internal models in current banking and insurance regulation, we further allow for belief heterogeneity in the market. The Pareto-optimal risk sharing game is solved through explicit construction. Competitive equilibria are established for some simple, yet natural settings. Results in the new framework are in sharp contrast to the classic utility-based risk sharing framework, and this possibly explains some financial phenomena observed during the 2007 - 09 financial crisis. Further, we investigate the issue 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.

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