Optimal Consumption and Portfolio Selection with Stochastic Differential Utility

Mark Schroder*, Costis Skiadas

*Corresponding author for this work

Research output: Contribution to journalArticlepeer-review

150 Scopus citations


We develop the utility gradient (or martingale) approach for computing portfolio and consumption plans that maximize stochastic differential utility (SDU), a continuous-time version of recursive utility due to D. Duffie and L. Epstein (1992, Econometrica60, 353-394). We characterize the first-order 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 continuous-time version of the CES Kreps-Porteus utilities studied by L. Epstein and A. Zin (1989, Econometrica57, 937-969). For this class, we derive closed-form 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. Journal of Economic Literature Classification Numbers: G11, E21, D91, D81, C61.

Original languageEnglish (US)
Pages (from-to)68-126
Number of pages59
JournalJournal of Economic Theory
Issue number1
StatePublished - Nov 1999

ASJC Scopus subject areas

  • Economics and Econometrics


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