This paper studies the problem of partially observed optimal control for forward-backward stochastic systems which are driven both by Brownian motions and an independent Poisson random measure. Combining forward-backw...This paper studies the problem of partially observed optimal control for forward-backward stochastic systems which are driven both by Brownian motions and an independent Poisson random measure. Combining forward-backward stochastic differential equation theory with certain classical convex variational techniques, the necessary maximum principle is proved for the partially observed optimal control, where the control domain is a nonempty convex set. Under certain convexity assumptions, the author also gives the sufficient conditions of an optimal control for the aforementioned optimal optimal problem. To illustrate the theoretical result, the author also works out an example of partial information linear-quadratic optimal control, and finds an explicit expression of the corresponding optimal control by applying the necessary and sufficient maximum principle.展开更多
基金This research is supported by the National Nature Science Foundation of China under Grant Nos 11001156, 11071144, the Nature Science Foundation of Shandong Province （ZR2009AQ017）, and Independent Innovation Foundation of Shandong University （IIFSDU）, China.
文摘This paper studies the problem of partially observed optimal control for forward-backward stochastic systems which are driven both by Brownian motions and an independent Poisson random measure. Combining forward-backward stochastic differential equation theory with certain classical convex variational techniques, the necessary maximum principle is proved for the partially observed optimal control, where the control domain is a nonempty convex set. Under certain convexity assumptions, the author also gives the sufficient conditions of an optimal control for the aforementioned optimal optimal problem. To illustrate the theoretical result, the author also works out an example of partial information linear-quadratic optimal control, and finds an explicit expression of the corresponding optimal control by applying the necessary and sufficient maximum principle.
