1. Efficient consumption set under recursive utility and unknown beliefs
- Author
-
Ali Lazrak, Fernando Zapatero, Sauder School of Business [British Columbia] (Sauder), University of British Columbia (UBC), FBE, Marshall School of Business, and University of Southern California (USC)
- Subjects
Economics and Econometrics ,Mathematical optimization ,050208 finance ,Partial differential equation ,recursive utility ,Applied Mathematics ,05 social sciences ,Markov process ,Exact differential equation ,[SHS.GESTION.FIN]Humanities and Social Sciences/Business administration/domain_shs.gestion.fin ,quadradtic backward stochastic differential equations ,beliefs ,martingale condition ,Homothetic transformation ,Stochastic partial differential equation ,Stochastic differential equation ,symbols.namesake ,Quadratic equation ,0502 economics and business ,Economics ,symbols ,Martingale (probability theory) ,Mathematical economics ,050205 econometrics - 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, Econometrica 60 (1992) 353]), 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.
- Published
- 2004