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Convex Risk Measures based on Divergence

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  • Paul Dommel
  • Alois Pichler

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.

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  • Paul Dommel & Alois Pichler, 2020. "Convex Risk Measures based on Divergence," Papers 2003.07648, arXiv.org, revised Mar 2020.
    • Handle: RePEc:arx:papers:2003.07648
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    References listed on IDEAS

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    1. Acerbi, Carlo, 2002. "Spectral measures of risk: A coherent representation of subjective risk aversion," Journal of Banking & Finance, Elsevier, vol. 26(7), pages 1505-1518, July.
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    Cited by:

    1. Rui Ding, 2023. "f-Betas and Portfolio Optimization with f-Divergence induced Risk Measures," Papers 2302.00452, arXiv.org, revised May 2023.

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