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Thursday, February 22, 2018 at 4:15pm
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.
Dr. Ruodu Wang is Associate Professor of Actuarial Science at the University of Waterloo in Canada. He received his Ph.D. in mathematics (2012) from the Georgia Institute of Technology, after completing his bachelor (2006) and Master's (2009) degrees in mathematics at Peking University. His research interest lies mainly in Quantitative Risk Management, and he has published more than 40 papers in leading academic journals in a wide variety of fields, including the Annals of Applied Probability, the Annals of Statistics, Operations Research, Statistical Science, Mathematics of Operations Research, Mathematical Finance, and Finance and Stochastics. He holds editorial positions of leading academic journals in actuarial science, including co-editor of the European Actuarial Journal (since August 2016), and co-editor of ASTIN Bulletin – The Journal of the International Actuarial Association (since January 2018). He is an affiliated member of RiskLab at ETH Zurich. His research is currently funded by the Natural Sciences and Engineering Research Council of Canada.