2019/10/01 by Mikhail Tselishchev, Tselishchev, Mikhail
Decision Sciences · Economics, Econometrics and Finance · Mathematics · #FOS: Economics and business #Fuzzy Systems and Optimization #Risk Management (q-fin.RM) #Risk and Portfolio Optimization #Stochastic processes and financial applications
paper · pdf · doi:10.48550/arxiv.1910.00640
openalex publication_date 2019/10/01 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
It is well known that Expected Shortfall (also called Average Value-at-Risk) is a convex risk measure, i. e. Expected Shortfall of a convex linear combination of arbitrary risk positions is not greater than a convex linear combination with the same weights of Expected Shortfalls of the same risk positions. In this short paper we prove that Expected Shortfall is a concave risk measure with respect to probability distributions, i. e. Expected Shortfall of a finite mixture of arbitrary risk positions is not lower than the linear combination of Expected Shortfalls of the same risk positions (with the same weights as in the mixture).