English

Linear-Quadratic Optimal Control Problem for Mean-Field Stochastic Differential Equations with a Type of Random Coefficients

Optimization and Control 2023-08-02 v1

Abstract

Motivated by linear-quadratic optimal control problems (LQ problems, for short) for mean-field stochastic differential equations (SDEs, for short) with the coefficients containing regime switching governed by a Markov chain, we consider an LQ problem for an SDE with the coefficients being adapted to a filtration independent of the Brownian motion driving the control system. Classical approach of completing the square is applied to the current problem and obvious shortcomings are indicated. Open-loop and closed-loop solvability are introduced and characterized.

Keywords

Cite

@article{arxiv.2308.00335,
  title  = {Linear-Quadratic Optimal Control Problem for Mean-Field Stochastic Differential Equations with a Type of Random Coefficients},
  author = {Hongwei Mei and Qingmeng Wei and Jiongmin Yong},
  journal= {arXiv preprint arXiv:2308.00335},
  year   = {2023}
}