Partially observed optimal controls of forward-backward doubly stochastic systems

Abstract

Abstract. The partially observed optimal control problem is considered for forward-backward doubly stochastic systems with controls entering into the diffusion and the observation. The maximum principle is proven for the partially observable optimal control problems. A probabilistic approach is used, and the adjoint processes are characterized as solutions of related forward-backward doubly stochastic differential equations in finite-dimensional spaces. Then, our theoretical result is applied to study a partially-observed linear-quadratic optimal control problem for a fully coupled forward-backward doubly stochastic system. Mathematics Subject Classification. 93E20, 60H10.

Optimal Control of Forward‐Backward Stochastic Jump‐Diffusion Differential Systems with Observation Noises: Stochastic Maximum Principle

“…A systematical account and an extensive list of references on partial observed stochastic optimal control for forward-backward stochastic systems can be found in a recent monograph Wang [26]. For other relevant developments in this regard, we refer the reader to the articles, such as [27][28][29][30][31], etc.…”

Optimal control of backward doubly stochastic system

“…Wu and Liu [20] proved the existence and uniqueness of solution to a kind of mean‐field BDSDE, and discussed partial information optimal control problem for backward doubly stochastic systems driven by Itô‐Lévy process of mean‐field type. Shi and Zhu [22] studied a partially observed optimal control of forward–backward doubly stochastic system. Moreover, Hui and Xiao [23] established a necessary condition and a sufficient condition for equilibrium point of non‐zero‐sum game and a saddle point of zero‐sum game, respectively.…”

Mean-Field Forward-Backward Doubly Stochastic Differential Equations and Related Nonlocal Stochastic Partial Differential Equations

“…[11]) and stochastic Hamiltonian systems arising in stochastic optimal control problems (cf. [12][13][14]).…”