Adjusted Rényi entropic Value-at-Risk

Abstract

Entropy is a measure of self information or uncertainty. Using different concepts of entropy, we may get different risk measures by dual representation. In this paper, we introduce and study the main properties of a class of convex risk measures, called as adjusted Rényi entropic Value-at-Risk (VaR). The adjusted risk measure quantifies risk as the minimum amount of capital that has to be raised and injected into a financial position to ensure that its Rényi entropic-VaR does not exceed a pre-specified threshold for every probability level. When p∈[1,∞), the adjusted Rényi entropic-VaR of order p is intimately linked to the (p+1)-increasing convex order by choosing the risk threshold to be the Rényi entropic-VaR of a benchmark random loss.