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Equivalence Between Time Consistency and Nested Formula

Author

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  • Henri G'erard

    (CERMICS)

  • Michel de Lara

    (CERMICS)

  • Jean-Philippe Chancelier

    (CERMICS, MATHRISK)

Abstract

You are a financial analyst. At the beginning of every week, you are able to rank every pair of stochastic processes starting from that week up to the horizon. Suppose that two processes are equal at the beginning of the week. Your ranking procedure is time consistent if the ranking does not change between this week and the next one. In this paper, we propose a minimalist definition of Time Consistency (TC) between two (assessment) mappings. With very few assumptions, we are able to prove an equivalence between Time Consistency and a Nested Formula (NF) between the two mappings. Thus, in a sense, two assessments are consistent if and only if one is factored into the other. We review the literature and observe that the various definitions of TC (or of NF) are special cases of ours, as they always include additional assumptions. By stripping off these additional assumptions, we present an overview of the literature where the contribution of each author is enlightened.

Suggested Citation

  • Henri G'erard & Michel de Lara & Jean-Philippe Chancelier, 2017. "Equivalence Between Time Consistency and Nested Formula," Papers 1711.08633, arXiv.org, revised May 2019.
  • Handle: RePEc:arx:papers:1711.08633
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    File URL: http://arxiv.org/pdf/1711.08633
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    References listed on IDEAS

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    1. Riedel, Frank, 2004. "Dynamic coherent risk measures," Stochastic Processes and their Applications, Elsevier, vol. 112(2), pages 185-200, August.
    2. Andrzej Ruszczyński & Alexander Shapiro, 2006. "Conditional Risk Mappings," Mathematics of Operations Research, INFORMS, vol. 31(3), pages 544-561, August.
    3. Epstein, Larry G. & Schneider, Martin, 2003. "Recursive multiple-priors," Journal of Economic Theory, Elsevier, vol. 113(1), pages 1-31, November.
    4. Stuart Dreyfus, 2002. "Richard Bellman on the Birth of Dynamic Programming," Operations Research, INFORMS, vol. 50(1), pages 48-51, February.
    5. Kreps, David M. & Porteus, Evan L., 1979. "Temporal von neumann-morgenstern and induced preferences," Journal of Economic Theory, Elsevier, vol. 20(1), pages 81-109, February.
    6. De Lara, Michel & Leclère, Vincent, 2016. "Building up time-consistency for risk measures and dynamic optimization," European Journal of Operational Research, Elsevier, vol. 249(1), pages 177-187.
    7. Bezalel Peleg & Menahem E. Yaari, 1973. "On the Existence of a Consistent Course of Action when Tastes are Changing," Review of Economic Studies, Oxford University Press, vol. 40(3), pages 391-401.
    8. Peter J. Hammond, 1976. "Changing Tastes and Coherent Dynamic Choice," Review of Economic Studies, Oxford University Press, vol. 43(1), pages 159-173.
    9. Kreps, David M & Porteus, Evan L, 1978. "Temporal Resolution of Uncertainty and Dynamic Choice Theory," Econometrica, Econometric Society, vol. 46(1), pages 185-200, January.
    10. Alexander Shapiro, 2016. "Rectangular Sets of Probability Measures," Operations Research, INFORMS, vol. 64(2), pages 528-541, April.
    11. 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.
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