Backward stochastic optimal control with mixed deterministic controller and random controller and its applications in linear-quadratic control

Huanjun Zhang and Zhiguo Yan

Applied Mathematics and Computation, 2020, vol. 369, issue C

Abstract: This paper investigates an optimal control problem driven by backward stochastic differential equation (BSDE) with two controllers – one is called deterministic controller and the other one is called random controller. Necessary and sufficient conditions for the mixed optimal control problem are derived. A linear-quadratic (LQ) case of the mixed optimal control problem is also studied. The mixed optimal controllers are explicitly expressed by the solution of a fully coupled mean-field forward–backward stochastic differential equation (SDE). One of novel features is that a kind of mean-field BSDE naturally arises from the research on the mixed optimal control problem. Finally, a product management problem is used to illustrate the theoretical results.

Keywords: Backward stochastic differential equation; Feedback expression of optimal control; Mean-field; Mixed deterministic and random control (search for similar items in EconPapers)
Date: 2020
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Citations: View citations in EconPapers (1)

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Persistent link: https://EconPapers.repec.org/RePEc:eee:apmaco:v:369:y:2020:i:c:s0096300319308343

DOI: 10.1016/j.amc.2019.124842

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