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Efficient Consumption Set Under Recursive Utility and Unknown Beliefs

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Author Info
Ali Lazrak
Fernando Zapatero
Abstract

In a context of complete financial markets where asset prices follow Ito's processes, we characterize the set of consumption processes which are optimal for a given stochastic differential utility (e.g. Duffie and Epstein (1992)) when beliefs are unknown. Necessary and sufficient conditions for the efficiency of a consumption process, consists of the existence of a solution to a quadratic backward stochastic differential equation and a martingale condition. We study the efficiency condition in the case of a class of homothetic stochastic differential utilities and derive some results for those particular cases. In a Markovian context, this efficiency condition becomes a partial differential equation.

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Paper provided by Quantitative Finance Research Centre, University of Technology, Sydney in its series Research Paper Series with number 85.

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Date of creation: 01 Jun 2002
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Handle: RePEc:uts:rpaper:85

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Related research
Keywords: recursive utility; quadradtic backward stochastic differential equations; beliefs; martingale condition;

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  1. Duffie, Darrell & Skiadas, Costis, 1994. "Continuous-time security pricing : A utility gradient approach," Journal of Mathematical Economics, Elsevier, vol. 23(2), pages 107-131, March. [Downloadable!] (restricted)
  2. Bick, Avi, 1990. " On Viable Diffusion Price Processes of the Market Portfolio," Journal of Finance, American Finance Association, vol. 45(2), pages 673-89, June. [Downloadable!] (restricted)
  3. He, Hua & Leland, Hayne, 1993. "On Equilibrium Asset Price Processes," Review of Financial Studies, Oxford University Press for Society for Financial Studies, vol. 6(3), pages 593-617. [Downloadable!] (restricted)
  4. P.A. Chiappori & I. Ekeland & F. Kubler & H.M. Polemarchakis, 2002. "Testable Implications of General Equilibrium Theory: a differentiable approach," Working Papers 2002-10, Brown University, Department of Economics. [Downloadable!]
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  5. Bick, Avi, 1987. "On the Consistency of the Black-Scholes Model with a General Equilibrium Framework," Journal of Financial and Quantitative Analysis, Cambridge University Press, vol. 22(03), pages 259-275, September. [Downloadable!]
  6. Cuoco, Domenico & Zapatero, Fernando, 2000. "On the Recoverability of Preferences and Beliefs," Review of Financial Studies, Oxford University Press for Society for Financial Studies, vol. 13(2), pages 417-31.
  7. Duffie, Darrell & Epstein, Larry G, 1992. "Stochastic Differential Utility," Econometrica, Econometric Society, vol. 60(2), pages 353-94, March. [Downloadable!] (restricted)
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