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
This paper considers the problem of partially observed optimal control for forward-backward stochastic systems driven by Brownian motions and an independent Poisson random measure with a feature that the cost function...This paper considers the problem of partially observed optimal control for forward-backward stochastic systems driven by Brownian motions and an independent Poisson random measure with a feature that the cost functional is of mean-field type. When the coefficients of the system and the objective performance functionals are allowed to be random, possibly non-Markovian, Malliavin calculus is employed to derive a maximum principle for the optimal control of such a system where the adjoint process is explicitly expressed. The authors also investigate the mean-field type optimal control problem for the system driven by mean-field type forward-backward stochastic differential equations(FBSDEs in short) with jumps, where the coefficients contain not only the state process but also its expectation under partially observed information. The maximum principle is established using convex variational technique. An example is given to illustrate the obtained results.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.
基金supported by the National Natural Science Foundation of China under Grant Nos.11471051 and 11371362the Teaching Mode Reform Project of BUPT under Grant No.BUPT2015JY52+5 种基金supported by the National Natural Science Foundation of China under Grant No.11371029the Natural Science Foundation of Anhui Province under Grant No.1508085JGD10supported by the National Natural Science Foundation of China under Grant No.71373043the National Social Science Foundation of China under Grant No.14AZD121the Scientific Research Project Achievement of UIBE NetworkingCollaboration Center for China’s Multinational Business under Grant No.201502YY003A
文摘This paper considers the problem of partially observed optimal control for forward-backward stochastic systems driven by Brownian motions and an independent Poisson random measure with a feature that the cost functional is of mean-field type. When the coefficients of the system and the objective performance functionals are allowed to be random, possibly non-Markovian, Malliavin calculus is employed to derive a maximum principle for the optimal control of such a system where the adjoint process is explicitly expressed. The authors also investigate the mean-field type optimal control problem for the system driven by mean-field type forward-backward stochastic differential equations(FBSDEs in short) with jumps, where the coefficients contain not only the state process but also its expectation under partially observed information. The maximum principle is established using convex variational technique. An example is given to illustrate the obtained results.
