An information-theoretic approach to constructing coherent risk measures

In the past decade, the new concept of coherent risk measure has found many applications in finance, insurance and operations research. In this paper, we introduce a new class of coherent risk measures constructed by using information-type pseudo-distances that generalize the Kullback-Leibler divergence, also known as the relative entropy. We first analyze the primal and dual representations of this class. We then study entropic value-at-risk (EVaR) which is the member of this class associated with relative entropy. We also show that conditional value-at-risk (CVaR), which is the most popular coherent risk measure, belongs to this class and is a lower bound for EVaR.