A maximum principle for mean-field stochastic control system with noisy observation. (March 2022)

• Record Type: Journal Article
• Authors: Wang, Guangchen; Wu, Zhen
• Is Part Of: Automatica. Volume 137(2022)
• Publication Date: 2022-03
• Subjects: Backward separation method -- Maximum principle -- Mean-field stochastic differential equation -- Optimal premium strategy in a feedback form -- Optimal filtering; Automatic control -- Periodicals; Automation -- Periodicals; 629.805
• DOI: 10.1016/j.automatica.2021.110135
• Languages: English
• ISSNs: 0005-1098

Abstract

Abstract: This paper is concerned with an optimal control problem driven by mean-field stochastic differential equation, where the state is partially observed via a noisy process. A new feature of the control problem is that the drift coefficient of observation equation is allowed to be a linear growth function, which immediately causes a difficulty in studying the control problem. A backward separation method with a dominated growth rate idea is used to overcome the difficulty. A maximum principle for optimality of the control problem is derived by an approximate technique. An asset–liability management problem for an insurance firm is studied. An optimal premium strategy in a feedback form is explicitly obtained.