Worst-case VaR and CVaR

Abstract

The main goal of this paper is to derive and compare values of worst-case VaR and CVaR under different type of information on distribution of random parameter. To this purpose we exploit results from moment problem theory and apply upper bound of loss probability of univariate random variable with special properties, given expected value and variance. Subsequently, we suppose that except the first two moments of the distributions, we know further characteristics of the class of distributions. We assume symmetry and/or unimodality. The bounds are also illustrated on the case of interbank exchange rate.