Risk measures under model uncertainty: a Bayesian viewpoint

Christa Cuchiero, Guido Gazzani and Irene Klein

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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.

Date: 2022-04
New Economics Papers: this item is included in nep-mic and nep-rmg
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Persistent link: https://EconPapers.repec.org/RePEc:arx:papers:2204.07115

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