Efficient Consumption Set Under Recursive Utility and Unknown Beliefs

Ali Lazrak and Fernando Zapatero
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Ali Lazrak: Sauder - Sauder School of Business [British Columbia] - UBC - University of British Columbia [Canada]
Fernando Zapatero: FBE, Marshall School of Business - USC - University of Southern California

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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.

Keywords: recursive utility; quadradtic backward stochastic differential equations; beliefs; martingale condition (search for similar items in EconPapers)
Date: 2004-02-02
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Citations: View citations in EconPapers (4)

Published in Journal of Mathematical Economics, 2004, Vol.40, n°1-2, pp.207-226. ⟨10.1016/S0304-4068(03)00088-0⟩

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Persistent link: https://EconPapers.repec.org/RePEc:hal:journl:hal-00485712

DOI: 10.1016/S0304-4068(03)00088-0

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