Abstract: The Value-at-Risk (VaR) and the Expected Shortfall (ES) are the two most popular risk measures used in banking and insurance regulation. In particular, according to the recent Basel Accords, ES replaces VaR as the standard risk measure for market risk in the banking sector. The class of VaR as quantile functions has been characterized in the literature with several different sets of economic axioms, whereas the class of ES, although being coherent risk measures, does not have an axiomatic foundation yet. We propose four intuitive and economically meaningful axioms to uniquely characterize an ES. In particular, a novel notion of risk concentration plays a significant role in the formulation of the axioms. Our results provide an economic support for using the Expected Shortfall as the globally dominating regulatory risk measure currently employed in Basel III/IV, as well as the ground for discussions on risk measurement for the future. If time permits, I will also discuss some recent results on the elicitation of ES, which may lead to alternative axiomatic formulations of ES.

Bio: Dr. Ruodu Wang is University Research Chair and Associate Professor of Actuarial Science at the University of Waterloo in Canada. He received his PhD in Mathematics (2012) from the Georgia Institute of Technology, after completing his Bachelor (2006) and Master's (2009) degrees at Peking University. His research interests include Quantitative Finance, Actuarial Science, Operations Research, and Risk Management, and has published over 50 papers in leading journals in the respective areas. He holds editorial positions of leading academic journals in Actuarial Science, including Co-Editor of ASTIN Bulletin - The Journal of the International Actuarial Association and Co-Editor of the European Actuarial Journal. He received one of Canada's 125 Discovery Accelerator Supplement Awards from the Natural Sciences and Engineering Research Council of Canada in 2018, and is an affiliated member of RiskLab at ETH Zurich.