A dynamic maximum principle for the optimization of recursive utilities under constraints

• 成果类型: Article
• 署名作者: El Karoui, N; Peng, S; Quenez, MC
• 署名单位: Institut Polytechnique de Paris; Ecole Polytechnique; Shandong University; Universite Gustave-Eiffel
• 刊物名称: ANNALS OF APPLIED PROBABILITY
• ISSN/ISSBN: 1050-5164
• 发表日期: 2001
• 页码: 664-693
• 关键词: STOCHASTIC DIFFERENTIAL-EQUATIONS; optimal consumption; PORTFOLIO POLICIES; incomplete markets; INVESTMENT; equilibrium; prices; MODEL

摘要

This paper examines the continuous-time portfolio-consumption problem of an agent with a recursive utility in the presence of nonlinear constraints on the wealth. Using backward stochastic differential equations, we state a dynamic maximum principle which generalizes the characterization of optimal policies obtained by Duffie and Skiadas [J. Math Econ. 23, 107-131 (1994)] in the case of a linear wealth. From this property, we derive a characterization of optimal wealth and utility processes as the unique solution of a forward-backward system. Existence of an optimal policy is also established via a penalization method.