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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. Lars Peter Hansen & Thomas J Sargent, 2014. "Robust Control and Model Misspecification," World Scientific Book Chapters, in: UNCERTAINTY WITHIN ECONOMIC MODELS, chapter 6, pages 155-216, World Scientific Publishing Co. Pte. Ltd..
    3. 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, July.
    4. Sujoy Mukerji & Jean-Marc Tallon, 2001. "Ambiguity Aversion and Incompleteness of Financial Markets," The Review of Economic Studies, Review of Economic Studies Ltd, vol. 68(4), pages 883-904.
    5. 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.
    6. Detlefsen, Kai & Scandolo, Giacomo, 2005. "Conditional and dynamic convex risk measures," SFB 649 Discussion Papers 2005-006, Humboldt University Berlin, Collaborative Research Center 649: Economic Risk.
    7. 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.
    8. Kai Detlefsen & Giacomo Scandolo, 2005. "Conditional and dynamic convex risk measures," Finance and Stochastics, Springer, vol. 9(4), pages 539-561, October.
    9. Gilboa, Itzhak & Schmeidler, David, 1989. "Maxmin expected utility with non-unique prior," Journal of Mathematical Economics, Elsevier, vol. 18(2), pages 141-153, April.
    10. Lars Peter Hansen & Thomas J Sargent, 2014. "Robust Control and Model Uncertainty," World Scientific Book Chapters, in: UNCERTAINTY WITHIN ECONOMIC MODELS, chapter 5, pages 145-154, World Scientific Publishing Co. Pte. Ltd..
    11. 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.
    12. 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.
    13. Wakai, Katsutoshi, 2007. "A note on recursive multiple-priors," Journal of Economic Theory, Elsevier, vol. 135(1), pages 567-571, July.
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    17. Daniel Ellsberg, 1961. "Risk, Ambiguity, and the Savage Axioms," The Quarterly Journal of Economics, President and Fellows of Harvard College, vol. 75(4), pages 643-669.
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    Full references (including those not matched with items on IDEAS)

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    More about this item

    Keywords

    Ambiguity Aversion; Model Uncertainty; Recursive Utility; Robust Control; Time Consistency;
    All these keywords.

    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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