Optimal consumption and portfolio selection with stochastic differential utility

• 成果类型: Article
• 署名作者: Schroder, M; Skiadas, C
• 署名单位: Michigan State University; Michigan State University's Broad College of Business; Northwestern University
• 刊物名称: JOURNAL OF ECONOMIC THEORY
• ISSN/ISSBN: 0022-0531
• DOI: 10.1006/jeth.1999.2558
• 发表日期: 1999
• 页码: 68-126

摘要

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, Econometrica 60. 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. Econometrica 57. 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. (C) 1999 Academic Press.