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 o...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].展开更多
This paper is concerned with partially-observed optimal control problems for stochastic delay systems. Combining Girsanov's theorem with a standard variational technique, the authors obtain a maximum principle on ...This paper is concerned with partially-observed optimal control problems for stochastic delay systems. Combining Girsanov's theorem with a standard variational technique, the authors obtain a maximum principle on the assumption that the system equation contains time delay and the control domain is convex. The related adjoint processes are characterized as solutions to anticipated backward stochastic differential equations in finite-dimensional spaces. Then, the proposed theoretical result is applied to study partially-observed linear-quadratic optimal control problem for stochastic delay system and an explicit observable control variable is given.展开更多
This paper is concerned with the optimal control problems of forward-backward delay systems involving impulse controls. The authors establish a stochastic maximum principle for this kind of systems. The most distingui...This paper is concerned with the optimal control problems of forward-backward delay systems involving impulse controls. The authors establish a stochastic maximum principle for this kind of systems. The most distinguishing features of the proposed problem are that the control variables consist of regular and impulsive controls, both with time delay, and that the domain of regular control is not necessarily convex. The authors obtain the necessary and sufficient conditions for optimal controls,which have potential applications in mathematical finance.展开更多
This paper discusses mean-field backward stochastic differentiM equations (mean-field BS- DEs) with jumps and a new type of controlled mean-field BSDEs with jumps, namely mean-field BSDEs with jumps strongly coupled...This paper discusses mean-field backward stochastic differentiM equations (mean-field BS- DEs) with jumps and a new type of controlled mean-field BSDEs with jumps, namely mean-field BSDEs with jumps strongly coupled with the value function of the associated control problem. The authors first prove the existence and the uniqueness as well as a comparison theorem for the above two types of BSDEs. For this the authors use an approximation method. Then, with the help of the notion of stochastic backward semigroups introduced by Peng in 1997, the authors get the dynamic programming principle (DPP) for the value functions. Furthermore, the authors prove that the value function is a viscosity solution of the associated nonlocal Hamilton-Jacobi-Bellman (HJB) integro-partial differential equation, which is unique in an adequate space of continuous functions introduced by Barles, et al. in 1997.展开更多
The authors discuss one type of general forward-backward stochastic differential equations (FBSDEs) with Ito's stochastic delayed equations as the forward equations and anticipated backward stochastic differential...The authors discuss one type of general forward-backward stochastic differential equations (FBSDEs) with Ito's stochastic delayed equations as the forward equations and anticipated backward stochastic differential equations as the backward equations.The existence and uniqueness results of the general FBSDEs are obtained.In the framework of the general FBSDEs in this paper,the explicit form of the optimal control for linear-quadratic stochastic optimal control problem with delay and the Nash equilibrium point for nonzero sum differential games problem with delay are obtained.展开更多
基金Project supported by the National Natural Science Foundation of China (No.10325101)the Science Foundation of China University of Mining and Technology.
文摘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].
文摘This paper is concerned with partially-observed optimal control problems for stochastic delay systems. Combining Girsanov's theorem with a standard variational technique, the authors obtain a maximum principle on the assumption that the system equation contains time delay and the control domain is convex. The related adjoint processes are characterized as solutions to anticipated backward stochastic differential equations in finite-dimensional spaces. Then, the proposed theoretical result is applied to study partially-observed linear-quadratic optimal control problem for stochastic delay system and an explicit observable control variable is given.
基金supported by the Natural Science Foundation of China under Grant No.61573217,111 Project(B12023)the National High-Level Personnel of Special Support Programthe Chang Jiang Scholar Program of Chinese Education Ministry
文摘This paper is concerned with the optimal control problems of forward-backward delay systems involving impulse controls. The authors establish a stochastic maximum principle for this kind of systems. The most distinguishing features of the proposed problem are that the control variables consist of regular and impulsive controls, both with time delay, and that the domain of regular control is not necessarily convex. The authors obtain the necessary and sufficient conditions for optimal controls,which have potential applications in mathematical finance.
基金supported by the National Natural Science Foundation of China under Grant Nos.11171187,11222110Shandong Province under Grant No.JQ201202+1 种基金Program for New Century Excellent Talents in University under Grant No.NCET-12-0331111 Project under Grant No.B12023
文摘This paper discusses mean-field backward stochastic differentiM equations (mean-field BS- DEs) with jumps and a new type of controlled mean-field BSDEs with jumps, namely mean-field BSDEs with jumps strongly coupled with the value function of the associated control problem. The authors first prove the existence and the uniqueness as well as a comparison theorem for the above two types of BSDEs. For this the authors use an approximation method. Then, with the help of the notion of stochastic backward semigroups introduced by Peng in 1997, the authors get the dynamic programming principle (DPP) for the value functions. Furthermore, the authors prove that the value function is a viscosity solution of the associated nonlocal Hamilton-Jacobi-Bellman (HJB) integro-partial differential equation, which is unique in an adequate space of continuous functions introduced by Barles, et al. in 1997.
基金Project supported by the 973 National Basic Research Program of China (No. 2007CB814904)the National Natural Science Foundations of China (No. 10921101)+2 种基金the Shandong Provincial Natural Science Foundation of China (No. 2008BS01024)the Science Fund for Distinguished Young Scholars of Shandong Province (No. JQ200801)the Shandong University Science Fund for Distinguished Young Scholars(No. 2009JQ004)
文摘The authors discuss one type of general forward-backward stochastic differential equations (FBSDEs) with Ito's stochastic delayed equations as the forward equations and anticipated backward stochastic differential equations as the backward equations.The existence and uniqueness results of the general FBSDEs are obtained.In the framework of the general FBSDEs in this paper,the explicit form of the optimal control for linear-quadratic stochastic optimal control problem with delay and the Nash equilibrium point for nonzero sum differential games problem with delay are obtained.