Efficient Consumption Set Under Recursive Utility and Unknown Beliefs
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.
|Date of creation:||01 Jun 2002|
|Date of revision:|
|Publication status:||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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