Optimal control of mean-field jump-diffusion systems with delay: A stochastic maximum principle approach

Qingxin Meng; Yang Shen

doi:10.1016/j.cam.2014.10.011

Optimal control of mean-field jump-diffusion systems with delay

A stochastic maximum principle approach

Qingxin Meng, Yang Shen^*

^*Corresponding author for this work

Research output: Contribution to journal › Article

33 Citations (Scopus)

Abstract

This paper is concerned with an optimal control problem under mean-field jump-diffusion systems with delay. Firstly, some existence and uniqueness results are proved for a jump-diffusion mean-field stochastic delay differential equation and a jump-diffusion mean-field advanced backward stochastic differential equation. Then necessary and sufficient maximum principles for control systems of mean-field type and with delay are established under certain conditions. A mean-field, delayed, linear-quadratic control problem is finally discussed using the obtained maximum principles.

Original language	English
Pages (from-to)	13-30
Number of pages	18
Journal	Journal of Computational and Applied Mathematics
Volume	279
DOIs	https://doi.org/10.1016/j.cam.2014.10.011
Publication status	Published - 1 May 2015
Externally published	Yes

Keywords

Advanced backward stochastic differential equation
Mean-field
Optimal control
Stochastic delay differential equation
Stochastic maximum principle

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title = "Optimal control of mean-field jump-diffusion systems with delay: A stochastic maximum principle approach",

abstract = "This paper is concerned with an optimal control problem under mean-field jump-diffusion systems with delay. Firstly, some existence and uniqueness results are proved for a jump-diffusion mean-field stochastic delay differential equation and a jump-diffusion mean-field advanced backward stochastic differential equation. Then necessary and sufficient maximum principles for control systems of mean-field type and with delay are established under certain conditions. A mean-field, delayed, linear-quadratic control problem is finally discussed using the obtained maximum principles.",

keywords = "Advanced backward stochastic differential equation, Mean-field, Optimal control, Stochastic delay differential equation, Stochastic maximum principle",

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AU - Shen, Yang

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Y1 - 2015/5/1

N2 - This paper is concerned with an optimal control problem under mean-field jump-diffusion systems with delay. Firstly, some existence and uniqueness results are proved for a jump-diffusion mean-field stochastic delay differential equation and a jump-diffusion mean-field advanced backward stochastic differential equation. Then necessary and sufficient maximum principles for control systems of mean-field type and with delay are established under certain conditions. A mean-field, delayed, linear-quadratic control problem is finally discussed using the obtained maximum principles.

AB - This paper is concerned with an optimal control problem under mean-field jump-diffusion systems with delay. Firstly, some existence and uniqueness results are proved for a jump-diffusion mean-field stochastic delay differential equation and a jump-diffusion mean-field advanced backward stochastic differential equation. Then necessary and sufficient maximum principles for control systems of mean-field type and with delay are established under certain conditions. A mean-field, delayed, linear-quadratic control problem is finally discussed using the obtained maximum principles.

KW - Advanced backward stochastic differential equation

KW - Mean-field

KW - Optimal control

KW - Stochastic delay differential equation

KW - Stochastic maximum principle

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