Partially observed optimal controls of forward-backward doubly stochastic systems∗
School of Mathematics, Shandong University,
2 School of Mathematics and Quantitative Economics, Shandong University of Finance and Economics, 250014 Jinan, P.R. China
Received: 5 January 2012
Revised: 22 August 2012
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
Key words: Forward-backward doubly stochastic system / partially observed optimal control / maximum principle / adjoint equation
This work was supported by National Natural Science Foundation of China (10771122, 11071145 and 11231005), Natural Science Foundation of Shandong Province of China (Y2006A08), Foundation for Innovative Research Groups of National Natural Science Foundation of China (10921101), National Basic Research Program of China (973 Program, 2007CB814900), Independent Innovation Foundation of Shandong University (2010JQ010), the 111 Project (B12023).
© EDP Sciences, SMAI, 2013