Linear quadratic control of backward stochastic differential equation with partial information

Guangchen Wang, Wencan Wang and Zhiguo Yan

Applied Mathematics and Computation, 2021, vol. 403, issue C

Abstract: In this paper, we study an optimal control problem of linear backward stochastic differential equation (BSDE) with quadratic cost functional under partial information. This problem is solved completely and explicitly by using a stochastic maximum principle and a decoupling technique. In terms of the maximum principle, a stochastic Hamiltonian system, which is a forward-backward stochastic differential equation (FBSDE) with filtering, is obtained. By decoupling the stochastic Hamiltonian system, three Riccati equations, a BSDE with filtering, and a stochastic differential equation (SDE) with filtering are derived. We then get a feedback representation of optimal control. An explicit formula for the corresponding optimal cost is also established. As illustrative examples, we consider two special scalar-valued control problems and give some numerical simulations.

Keywords: Linear quadratic optimal control; Backward stochastic differential equation; Filtering; Ricatti equation; Feedback representation (search for similar items in EconPapers)
Date: 2021
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Citations: View citations in EconPapers (3)

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Persistent link: https://EconPapers.repec.org/RePEc:eee:apmaco:v:403:y:2021:i:c:s009630032100254x

DOI: 10.1016/j.amc.2021.126164

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