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Risk measures under model uncertainty: a Bayesian viewpoint

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  • Christa Cuchiero
  • Guido Gazzani
  • Irene Klein

Abstract

We introduce two kinds of risk measures with respect to some reference probability measure, which both allow for a certain order structure and domination property. Analyzing their relation to each other leads to the question when a certain minimax inequality is actually an equality. We then provide conditions under which the corresponding robust risk measures, being defined as the supremum over all risk measures induced by a set of probability measures, can be represented classically in terms of one single probability measure. We focus in particular on the mixture probability measure obtained via mixing over a set of probability measures using some prior, which represents for instance the regulator's beliefs. The classical representation in terms of the mixture probability measure can then be interpreted as a Bayesian approach to robust risk measures.

Suggested Citation

  • Christa Cuchiero & Guido Gazzani & Irene Klein, 2022. "Risk measures under model uncertainty: a Bayesian viewpoint," Papers 2204.07115, arXiv.org.
    • Handle: RePEc:arx:papers:2204.07115
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    References listed on IDEAS

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