Comparative analyses of expected shortfall and value-at-risk

This paper summarizes the authors' papers on the comparative analyses of expected shortfall and value-at-risk. It discusses the properties of risk measures in terms of (1) elimination of tail risk; (2) consistency with expected utility maximization; (3) subadditivity (convexity); and (4) stability on estimation. It examines whether expected shortfall and value-at-risk satisfy these properties, and shows that expected shortfall is superior to value-at-risk in terms of (1), (2), and (3), but inferior to value-at-risk in terms of (4).