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Entropic Value-at-Risk: A New Coherent Risk Measure
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Journal Article
Entropic Value-at-Risk: A New Coherent Risk Measure
2012
Overview
This paper introduces the concept of
entropic value-at-risk
(EVaR), a new coherent risk measure that corresponds to the tightest possible upper bound obtained from the Chernoff inequality for the
value-at-risk
(VaR) as well as the
conditional value-at-risk
(CVaR). We show that a broad class of stochastic optimization problems that are computationally intractable with the CVaR is efficiently solvable when the EVaR is incorporated. We also prove that if two distributions have the same EVaR at all confidence levels, then they are identical at all points. The dual representation of the EVaR is closely related to the Kullback-Leibler divergence, also known as the relative entropy. Inspired by this dual representation, we define a large class of coherent risk measures, called
g-entropic
risk measures. The new class includes both the CVaR and the EVaR.
Publisher
Springer US,Springer Nature B.V
