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On the Recoverability of Preferences and Beliefs

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  • Cuoco, Domenico
  • Zapatero, Fernando

Abstract

We examine the extent to which an investor's tastes and beliefs can be jointly recovered from knowledge of his/her consumption choice. More precisely, we assume that the investor's preferences admit an expected utility representation, but with subjective (unknown) probabilities, and investigate what joint restrictions can be placed on utility functions and beliefs. If the investor draws utility from intertemporal consumption, we show that the set of utility functions and beliefs that are consistent with a given consumption choice can be characterized by a martingale condition. In the Markovian case, this characterization can be restated in terms of a Riccati differential equation that must be satisfied by the investor's relative risk aversion function. To each solution of this differential equation is associated a unique utility function and a unique set of beliefs supporting the given consumption choice. Moreover, we show that the differential equation has at most one solution in the class of utility functions displaying infinite absolute risk aversion at the origin. Thus, preferences (and associated beliefs) can be uniquely recovered within this class. Article published by Oxford University Press on behalf of the Society for Financial Studies in its journal, The Review of Financial Studies.

Suggested Citation

  • Cuoco, Domenico & Zapatero, Fernando, 2000. "On the Recoverability of Preferences and Beliefs," The Review of Financial Studies, Society for Financial Studies, vol. 13(2), pages 417-431.
    • Handle: RePEc:oup:rfinst:v:13:y:2000:i:2:p:417-31
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    Cited by:

    1. Robert Nau, 2001. "De Finetti was Right: Probability Does Not Exist," Theory and Decision, Springer, vol. 51(2), pages 89-124, December.
    2. Lüders, Erik, 2002. "Asset Prices and Alternative Characterizations of the Pricing Kernel," ZEW Discussion Papers 02-10, ZEW - Leibniz Centre for European Economic Research.
    3. Mele, Antonio, 2004. "General Properties of Rational Stock-Market Fluctuations," Economics Series 153, Institute for Advanced Studies.
    4. Felix Kubler & Karl Schmedders, 2010. "Non-parametric counterfactual analysis in dynamic general equilibrium," Economic Theory, Springer;Society for the Advancement of Economic Theory (SAET), vol. 45(1), pages 181-200, October.
    5. Lazrak, Ali & Zapatero, Fernando, 2004. "Efficient consumption set under recursive utility and unknown beliefs," Journal of Mathematical Economics, Elsevier, vol. 40(1-2), pages 207-226, February.

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