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Partially observed optimal controls of forward-backward doubly stochastic systems

  • Yufeng Shi (a1) and Qingfeng Zhu (a1) (a2)

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.

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