Optimal Consumption and Portfolio Selection with Stochastic Differential Utility

KGSM, Department of Finance Working Paper No. 226

62 Pages Posted: 19 Feb 1999

Date Written: March 1999


This paper develops 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 Duffie and Epstein (1992a). The setting is that of a general stochastic investment opportunity set with Brownian information (making some of the results novel in the time-additive case, as well). We characterize the first order conditions of optimality as a system of forward-backward SDE's, and for the Markovian case we show how to solve this system in terms of a system of quasilinear parabolic PDE's and forward only SDE's, which is amenable to numerical computation. Another contribution is a proof of existence, uniqueness, and basic properties for a parametric class of homothetic SDU that can be thought of as a continuous-time version of the CES Kreps-Porteus utilities studied by Epstein and Zin (1989). For this class, we show that the solution method simplifies significantly, resulting in closed form solutions in terms of a single backward SDE (without imposing a Markovian structure). The latter can be easily computed, as we will illustrate with a number of tractable concrete examples involving the type of "affine" state price dynamics that are familiar from the term structure literature.

JEL Classification: G1, D9, E2, C6

Suggested Citation

Schroder, Mark D. and Skiadas, Costis, Optimal Consumption and Portfolio Selection with Stochastic Differential Utility (March 1999). KGSM, Department of Finance Working Paper No. 226. Available at SSRN: https://ssrn.com/abstract=148148 or http://dx.doi.org/10.2139/ssrn.148148

Mark D. Schroder

Michigan State University - The Eli Broad Graduate School of Management ( email )

323 Eppley Center
East Lansing, MI 48824-1121
United States
517-432-0622 (Phone)
517-432-1080 (Fax)

Costis Skiadas (Contact Author)

Northwestern University - Kellogg School of Management ( email )

2001 Sheridan Road
Evanston, IL 60208
United States
847-467-2328 (Phone)
847-491-5719 (Fax)

HOME PAGE: http://www.kellogg.northwestern.edu/faculty/skiadas/research/research.htm

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