Efficient Consumption Set Under Recursive Utility and Unknown Beliefs

Ali Lazrak and Fernando Zapatero

No 85, Research Paper Series from Quantitative Finance Research Centre, University of Technology, Sydney

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)
Pages: 20 pages
Date: 2002-06-01
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Published as: Lazrak, A. and Zapatero, F., 2004, "Efficient Consumption Set Under Recursive Utility and Unknown Beliefs", Journal of Mathematical Economics, 40(1-2), 207-226.

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Journal Article: Efficient consumption set under recursive utility and unknown beliefs (2004)
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