An optimal control problem for mean-field forward–backward stochastic differential equation with noisy observation. (December 2017)

• Record Type: Journal Article
• Authors: Wang, Guangchen; Xiao, Hua; Xing, Guojing
• Is Part Of: Automatica. Volume 86(2017)
• Page Start: 104
• Page End: 109
• Publication Date: 2017-12
• Subjects: Backward separation method -- Maximum principle -- Mean-field forward–backward stochastic differential equation -- Optimal filter -- Recursive utility; Automatic control -- Periodicals; Automation -- Periodicals; 629.805
• DOI: 10.1016/j.automatica.2017.07.018
• Languages: English
• ISSNs: 0005-1098

Abstract

Abstract: This article is concerned with an optimal control problem derived by mean-field forward–backward stochastic differential equation with noisy observation, where the drift coefficients of the state equation and the observation equation are linear with respect to the state and its expectation. The control problem is different from the existing literature concerning optimal control for mean-field stochastic systems, and has more applications in mathematical finance, e.g., asset–liability management problem with recursive utility, systematic risk model. Using a backward separation method with a decomposition technique, two optimality conditions along with two coupled forward–backward optimal filters are derived. Linear–quadratic optimal control problems for mean-field forward–backward stochastic differential equations are studied.