2025/07/20 by Jialong Li, Zhiyong Yu, Li, Jialong +3
Economics, Econometrics and Finance · Computer Science · Engineering · #Stochastic processes and financial applications #Optimization and Variational Analysis #Stability and Control of Uncertain Systems
paper · pdf · doi:10.48550/arxiv.2507.14992
This paper is concerned with a kind of linear-quadratic (LQ) optimal control problem of backward stochastic differential equation (BSDE) with partial information. The cost functional includes cross terms between the state and control, and the weighting matrices are allowed to be indefinite. Through variational methods and stochastic filtering techniques, we derive the necessary and sufficient conditions for the optimal control, where a Hamiltonian system plays a crucial role. Moreover, to construct the optimal control, we introduce a matrix-valued differential equation and a BSDE with filtering, and establish their solvability under the assumption that the cost functional is uniformly convex. Finally, we present explicit forms of the optimal control and value function.