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Efficient Consumption Set Under Recursive Utility and Unknown Beliefs

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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Submitted on : Friday, May 21, 2010 - 3:22:33 PM
Last modification on : Friday, December 18, 2020 - 5:30:02 PM

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Ali Lazrak, Fernando Zapatero. Efficient Consumption Set Under Recursive Utility and Unknown Beliefs. Journal of Mathematical Economics, Elsevier, 2004, Vol.40, n°1-2, pp.207-226. ⟨10.1016/S0304-4068(03)00088-0⟩. ⟨hal-00485712⟩

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