UTILITY MAXIMIZATION VIA DECOUPLING FIELDS

• 成果类型: Article
• 署名作者: Fromm, Alexander; Imkeller, Peter
• 署名单位: Friedrich Schiller University of Jena; Humboldt University of Berlin
• 刊物名称: ANNALS OF APPLIED PROBABILITY
• ISSN/ISSBN: 1050-5164
• DOI: 10.1214/20-AAP1569
• 发表日期: 2020
• 页码: 2665-2694
• 关键词: STOCHASTIC DIFFERENTIAL-EQUATIONS; BACKWARD

摘要

We consider the utility maximization problem for a general class of utility functions defined on the real line. We rely on existing results which reduce the problem to a coupled forward-backward stochastic differential equation (FBSDE) and concentrate on showing existence and uniqueness of solution processes to this FBSDE. We use the method of decoupling fields for strongly coupled, multi-dimensional and possibly non-Lipschitz systems as the central technique in conducting the proofs.