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Coherent multiperiod risk adjusted values and Bellman’s principle

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  • Philippe Artzner
  • Freddy Delbaen
  • Jean-Marc Eber
  • David Heath
  • Hyejin Ku

Abstract

Starting with a time-0 coherent risk measure defined for “value processes”, we also define risk measurement processes. Two other constructions of measurement processes are given in terms of sets of test probabilities. These latter constructions are identical and are related to the former construction when the sets fulfill a stability condition also met in multiperiod treatment of ambiguity as in decision-making. We finally deduce risk measurements for the final value of locked-in positions and repeat a warning concerning Tail-Value-at-Risk. Copyright Springer Science+Business Media, LLC 2007

Suggested Citation

  • Philippe Artzner & Freddy Delbaen & Jean-Marc Eber & David Heath & Hyejin Ku, 2007. "Coherent multiperiod risk adjusted values and Bellman’s principle," Annals of Operations Research, Springer, vol. 152(1), pages 5-22, July.
    • Handle: RePEc:spr:annopr:v:152:y:2007:i:1:p:5-22:10.1007/s10479-006-0132-6
    DOI: 10.1007/s10479-006-0132-6
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    References listed on IDEAS

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    1. Wang, Tan, 2003. "Conditional preferences and updating," Journal of Economic Theory, Elsevier, vol. 108(2), pages 286-321, February.
    2. Wilkie, A. D. & Waters, H. R. & Yang, S., 2003. "Reserving, Pricing and Hedging For Policies with Guaranteed Annuity Options," British Actuarial Journal, Cambridge University Press, vol. 9(2), pages 263-391, June.
    3. Gilboa, Itzhak & Schmeidler, David, 1989. "Maxmin expected utility with non-unique prior," Journal of Mathematical Economics, Elsevier, vol. 18(2), pages 141-153, April.
    4. Dothan, Michael U., 1990. "Prices in Financial Markets," OUP Catalogue, Oxford University Press, number 9780195053128, Decembrie.
    5. Yumiharu Nakano, 2003. "Minimizing coherent risk measures of shortfall in discrete-time models with cone constraints," Applied Mathematical Finance, Taylor & Francis Journals, vol. 10(2), pages 163-181.
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