Mathematical Methods of Operations Research

, Volume 63, Issue 1, pp 169–186 | Cite as

Time Consistent Dynamic Risk Measures

Original Article
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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.

Keywords

Time consistency Multi-stage Target-percentile Value-at-risk Conditional value-at-risk Markov decision process 
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Copyright information

© Springer-Verlag 2006

Authors and Affiliations

  1. 1.Center for Industrial and Applied Mathematics, School of Mathematics & StatisticsUniversity of South AustraliaMawson LakesAustralia

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