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Time Consistent Dynamic Risk Measures

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Abstract

We introduce the time-consistency concept that is inspired by the so-called “principle of optimality” of dynamic programming and demonstrate – via an example – that the conditional value-at-risk (CVaR) need not be time-consistent in a multi-stage case. Then, we give the formulation of the target-percentile risk measure which is time-consistent and hence more suitable in the multi-stage investment context. Finally, we also generalize the value-at-risk and CVaR to multi-stage risk measures based on the theory and structure of the target-percentile risk measure.

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Authors and Affiliations

  1. Center for Industrial and Applied Mathematics, School of Mathematics & Statistics, University of South Australia, Mawson Lakes, SA, 5095, Australia

    Kang Boda & Jerzy A. Filar

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  1. Kang Boda
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  2. Jerzy A. Filar
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Correspondence to Jerzy A. Filar.

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Boda, K., Filar, J.A. Time Consistent Dynamic Risk Measures. Math Meth Oper Res 63, 169–186 (2006). https://doi.org/10.1007/s00186-005-0045-1

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  • DOI: https://doi.org/10.1007/s00186-005-0045-1

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