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Time Consistent Dynamic Risk Measures

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  • Kang Boda
  • Jerzy Filar

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. Copyright Springer-Verlag 2006

Suggested Citation

  • Kang Boda & Jerzy Filar, 2006. "Time Consistent Dynamic Risk Measures," Mathematical Methods of Operations Research, Springer;Gesellschaft für Operations Research (GOR);Nederlands Genootschap voor Besliskunde (NGB), vol. 63(1), pages 169-186, February.
    • Handle: RePEc:spr:mathme:v:63:y:2006:i:1:p:169-186
    DOI: 10.1007/s00186-005-0045-1
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    References listed on IDEAS

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    1. Philippe Artzner & Freddy Delbaen & Jean‐Marc Eber & David Heath, 1999. "Coherent Measures of Risk," Mathematical Finance, Wiley Blackwell, vol. 9(3), pages 203-228, July.
    2. Ronald A. Howard & James E. Matheson, 1972. "Risk-Sensitive Markov Decision Processes," Management Science, INFORMS, vol. 18(7), pages 356-369, March.
    3. Jerzy A. Filar & L. C. M. Kallenberg & Huey-Miin Lee, 1989. "Variance-Penalized Markov Decision Processes," Mathematics of Operations Research, INFORMS, vol. 14(1), pages 147-161, February.
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