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

Author

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  • Bäuerle Nicole
  • Mundt André

    (University of Karlsruhe (TH), Institute for Stochastics, Karlsruhe)

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.

Suggested Citation

  • Bäuerle Nicole & Mundt André, 2009. "A Bayesian approach to incorporate model ambiguity in a dynamic risk measure," Statistics & Risk Modeling, De Gruyter, vol. 26(3), pages 219-242, April.
    • Handle: RePEc:bpj:strimo:v:26:y:2009:i:3:p:219-242:n:3
    DOI: 10.1524/stnd.2008.1000
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    References listed on IDEAS

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