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Convex Risk Measures based on Divergence

Paul Dommel and Alois Pichler

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Abstract: Risk measures connect probability theory or statistics to optimization, particularly to convex optimization. They are nowadays standard in applications of finance and in insurance involving risk aversion. This paper investigates a wide class of risk measures on Orlicz spaces. The characterizing function describes the decision maker's risk assessment towards increasing losses. We link the risk measures to a crucial formula developed by Rockafellar for the Average Value-at-Risk based on convex duality, which is fundamental in corresponding optimization problems. We characterize the dual and provide complementary representations.

Date: 2020-03, Revised 2020-03
New Economics Papers: this item is included in nep-rmg
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Handle: RePEc:arx:papers:2003.07648