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Dynamic Variational Preferences

Author

Listed:
  • Fabio Maccheroni
  • Massimo Marinacci
  • Aldo Rustichini

Abstract

We introduce and axiomatize dynamic variational preferences, the dynamic version of the variational preferences we axiomatized in [21], which generalize the multiple priors preferences of Gilboa and Schmeidler [9], and include the Multiplier Preferences inspired by robust control and first used in macroeconomics by Hansen and Sargent (see [11]), as well as the classic Mean Variance Preferences of Markovitz and Tobin. We provide a condition that makes dynamic variational preferences time consistent, and their representation recursive. This gives them the analytical tractability needed in macroeconomic and financial applications. A corollary of our results is that Multiplier Preferences are time consistent, but Mean Variance Preferences are not.

Suggested Citation

  • Fabio Maccheroni & Massimo Marinacci & Aldo Rustichini, 2006. "Dynamic Variational Preferences," Carlo Alberto Notebooks 1, Collegio Carlo Alberto.
    • Handle: RePEc:cca:wpaper:1
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    References listed on IDEAS

    as
    1. Wang, Tan, 2003. "Conditional preferences and updating," Journal of Economic Theory, Elsevier, vol. 108(2), pages 286-321, February.
    2. Dow, James & Werlang, Sergio Ribeiro da Costa, 1992. "Uncertainty Aversion, Risk Aversion, and the Optimal Choice of Portfolio," Econometrica, Econometric Society, vol. 60(1), pages 197-204, January.
    3. Fabio Maccheroni & Massimo Marinacci & Aldo Rustichini, 2004. "Variational representation of preferences under ambiguity," ICER Working Papers - Applied Mathematics Series 05-2004, ICER - International Centre for Economic Research.
    4. Epstein, Larry G. & Schneider, Martin, 2003. "Recursive multiple-priors," Journal of Economic Theory, Elsevier, vol. 113(1), pages 1-31, November.
    5. Fabio Maccheroni & Massimo Marinacci & Aldo Rustichini & Marco Taboga, 2009. "Portfolio Selection With Monotone Mean-Variance Preferences," Mathematical Finance, Wiley Blackwell, vol. 19(3), pages 487-521.
    6. Thomas J. Sargent & LarsPeter Hansen, 2001. "Robust Control and Model Uncertainty," American Economic Review, American Economic Association, vol. 91(2), pages 60-66, May.
    7. Epstein, Larry G & Wang, Tan, 1994. "Intertemporal Asset Pricing Under Knightian Uncertainty," Econometrica, Econometric Society, vol. 62(2), pages 283-322, March.
    8. Sujoy Mukerji & Jean-Marc Tallon, 2001. "Ambiguity Aversion and Incompleteness of Financial Markets," Review of Economic Studies, Oxford University Press, vol. 68(4), pages 883-904.
    9. Hart, Sergiu & Modica, Salvatore & Schmeidler, David, 1990. "A Neo2Bayesian Foundation of the Maximin Value for Two-Person Zero- Sum Games," Foerder Institute for Economic Research Working Papers 275500, Tel-Aviv University > Foerder Institute for Economic Research.
    10. Wakai, Katsutoshi, 2007. "A note on recursive multiple-priors," Journal of Economic Theory, Elsevier, vol. 135(1), pages 567-571, July.
    11. Takashi Hayashi, 2005. "Intertemporal substitution, risk aversion and ambiguity aversion," Economic Theory, Springer;Society for the Advancement of Economic Theory (SAET), vol. 25(4), pages 933-956, June.
    12. Kai Detlefsen & Giacomo Scandolo, 2005. "Conditional and dynamic convex risk measures," Finance and Stochastics, Springer, vol. 9(4), pages 539-561, October.
    13. Hayashi, Takashi, 2003. "Quasi-stationary cardinal utility and present bias," Journal of Economic Theory, Elsevier, vol. 112(2), pages 343-352, October.
    14. Gilboa, Itzhak & Schmeidler, David, 1986. "Maxmin Expected Utility with a Non-Unique Prior," Foerder Institute for Economic Research Working Papers 275405, Tel-Aviv University > Foerder Institute for Economic Research.
    15. Kai Detlefsen & Giacomo Scandolo, 2005. "Conditional and Dynamic Convex Risk Measures," SFB 649 Discussion Papers SFB649DP2005-006, Sonderforschungsbereich 649, Humboldt University, Berlin, Germany.
    16. Gilboa, Itzhak & Schmeidler, David, 1989. "Maxmin expected utility with non-unique prior," Journal of Mathematical Economics, Elsevier, vol. 18(2), pages 141-153, April.
    17. Hansen, Lars Peter & Sargent, Thomas J. & Turmuhambetova, Gauhar & Williams, Noah, 2006. "Robust control and model misspecification," Journal of Economic Theory, Elsevier, vol. 128(1), pages 45-90, May.
    18. Paolo Ghirardato & Fabio Maccheroni & Massimo Marinacci, 2002. "Ambiguity from the Differential Viewpoint," ICER Working Papers - Applied Mathematics Series 17-2002, ICER - International Centre for Economic Research.
    19. Daniel Ellsberg, 1961. "Risk, Ambiguity, and the Savage Axioms," The Quarterly Journal of Economics, Oxford University Press, vol. 75(4), pages 643-669.
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    More about this item

    Keywords

    Ambiguity Aversion; Model Uncertainty; Recursive Utility; Robust Control; Time Consistency;

    JEL classification:

    • C61 - Mathematical and Quantitative Methods - - Mathematical Methods; Programming Models; Mathematical and Simulation Modeling - - - Optimization Techniques; Programming Models; Dynamic Analysis
    • D81 - Microeconomics - - Information, Knowledge, and Uncertainty - - - Criteria for Decision-Making under Risk and Uncertainty

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