A Bayesian approach to incorporate model ambiguity in a dynamic risk measure

Bäuerle Nicole and Mundt André
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Mundt André: University of Karlsruhe (TH), Institute for Stochastics, Karlsruhe

Statistics & Risk Modeling, 2009, vol. 26, issue 3, 219-242

Abstract: In this paper we consider an explicit dynamic risk measure for discrete-time payment processes which have a Markovian structure. The risk measure is essentially a sum of conditional Average Value-at-Risks. Analogous to the static Average Value-at-Risk, this risk measures can be reformulated in terms of the value functions of a dynamic optimization problem, namely a so-called Markov decision problem. This observation gives a nice recursive computation formula. Afterwards, the definition of the dynamic risk measure is generalized to a setting with incomplete information about the risk distribution which can be seen as model ambiguity. We choose a parametric approach here. The dynamic risk measure is again defined as the sum of conditional Average Value-at-Risks or equivalently is the solution of a Bayesian decision problem. Finally, it is possible to discuss the effect of model ambiguity on the risk measure: Surprisingly, it may be the case that the risk decreases when additional “risk” due to parameter uncertainty shows up. All investigations are illustrated by a simple but useful coin tossing game proposed by Artzner and by the classical Cox–Ross–Rubinstein model.

Keywords: dynamic risk measure; Markov decision process; incomplete information; Bayesian approach; average value-at-risk (search for similar items in EconPapers)
Date: 2009
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Persistent link: https://EconPapers.repec.org/RePEc:bpj:strimo:v:26:y:2009:i:3:p:219-242:n:3

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DOI: 10.1524/stnd.2008.1000

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