Results 1 
1 of
1
Optimal Consumption and Portfolio Selection with Stochastic Differential Utility
, 1999
"... We develop the utility gradient (or martingale) approach for computing portfolio and consumption plans that maximize stochastic differential utility (SDU), a continuoustime version of recursive utility due to D. Duffie and L. Epstein (1992, Econometrica 60, 353 394). We characterize the firstorder ..."
Abstract

Cited by 79 (4 self)
 Add to MetaCart
We develop the utility gradient (or martingale) approach for computing portfolio and consumption plans that maximize stochastic differential utility (SDU), a continuoustime version of recursive utility due to D. Duffie and L. Epstein (1992, Econometrica 60, 353 394). We characterize the firstorder conditions of optimality as a system of forward backward SDEs, which, in the Markovian case, reduces to a system of PDEs and forward only SDEs that is amenable to numerical computation. Another contribution is a proof of existence, uniqueness, and basic properties for a parametric class of homothetic SDUs that can be thought of as a continuoustime version of the CES Kreps Porteus utilities studied by L. Epstein and A. Zin (1989, Econometrica 57, 937 969). For this class, we derive closedform solutions in terms of a single backward SDE (without imposing a Markovian structure). We conclude with several tractable concrete examples involving the type of ``affine'' state price dynamics that are familiar from the term structure literature.