The paper is concerned with a stochastic optimal control problem in which the controlled system is described by a fully coupled nonlinear forward-backward stochastic differential equation driven by a Brownian motion.It is required that all admissible control processes are adapted to a given subfiltration of the filtration generated by the underlying Brownian motion.For this type of partial information control,one sufficient(a verification theorem) and one necessary conditions of optimality are proved.The control domain need to be convex and the forward diffusion coefficient of the system can contain the control variable.
MENG QingXin1,2 1 Department of Mathematical Sciences,Huzhou University,Zhejiang 313000,China 2 Institute of Mathematics,Fudan University,Shanghai 200433,China
The paper is concerned with a stochastic optimal control problem where the controlled systems are driven by Teugel＇s martingales and an independent multi-dimensional Brownian motion, Necessary and sufficient conditions for an optimal control of the control problem with the control domain being convex are proved by the classical method of convex variation, and the coefficients appearing in the systems are allowed to depend on the control variables, As an application, the linear quadratic stochastic optimal control problem is studied.
framework in the risk uniqueness In this paper, properties of the entropic risk measure are examined rigorously in a general This risk measure is then applied in a dynamic portfolio optimization problem, appearing management constraint. By considering the dual problem, we prove the existence and of the solution and obtain an analytic expression for the solution.
Under the Lipschitz assumption and square integrable assumption on g, the author proves that Jensen＇s inequality holds for backward stochastic differential equations with generator g if and only if g is independent of y, g（t, 0）≡ 0 and g is super homogeneous with respect to z. This result generalizes the known results on Jensen＇s inequality for gexpectation in [4, 7-9].
Long JIANG Department of Mathematics, China University of Mining and Technology, Xuzhou 221008, Jiangsu, China
