In this paper, we use the solutions of forward-backward stochastic differential equations to get the explicit form of the optimal control for linear quadratic stochastic optimal control problem and the open-loop Nash ...In this paper, we use the solutions of forward-backward stochastic differential equations to get the explicit form of the optimal control for linear quadratic stochastic optimal control problem and the open-loop Nash equilibrium point for nonzero sum differential games problem. We also discuss the solvability of the generalized Riccati equation system and give the linear feedback regulator for the optimal control problem using the solution of this kind of Riccati equation system.展开更多
The existence and uniqueness of the solutions for one kind of forward- backward stochastic differential equations with Brownian motion and Poisson process as the noise source were given under the monotone conditions. ...The existence and uniqueness of the solutions for one kind of forward- backward stochastic differential equations with Brownian motion and Poisson process as the noise source were given under the monotone conditions. Then these results were applied to nonzero-sum differential games with random jumps to get the explicit form of the open-loop Nash equilibrium point by the solution of the forward-backward stochastic differential equations.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
In this paper,a leader-follower stochastic differential game is studied for a linear stochastic differential equation with quadratic cost functionals.The coefficients in the state equation and the weighting matrices i...In this paper,a leader-follower stochastic differential game is studied for a linear stochastic differential equation with quadratic cost functionals.The coefficients in the state equation and the weighting matrices in the cost functionals are all deterministic.Closed-loop strategies are introduced,which require to be independent of initial states;and such a nature makes it very useful and convenient in applications.The follower first solves a stochastic linear quadratic optimal control problem,and his optimal closed-loop strategy is characterized by a Riccati equation,together with an adapted solution to a linear backward stochastic differential equation.Then the leader turns to solve a stochastic linear quadratic optimal control problem of a forward-backward stochastic differential equation,necessary conditions for the existence of the optimal closed-loop strategy for the leader is given by a Riccati equation.Some examples are also given.展开更多
The existence and uniqueness of the solutions for one kind of forward-backward stochastic differential equations with Brownian motion and Poisson process as the noise source were given under the monotone conditions.Th...The existence and uniqueness of the solutions for one kind of forward-backward stochastic differential equations with Brownian motion and Poisson process as the noise source were given under the monotone conditions.Then these results were applied to nonzero-sum differential games with random jumps to get the explicit form of the open-loop Nash equilibrium point by the solution of the forward-backward stochastic differential equations.展开更多
This paper constructs a non-cooperative/cooperative stochasticdifferential game model to prove that the optimal strategies trajectory ofagents in a system with a topological configuration of a Multi-Local-Worldgraph w...This paper constructs a non-cooperative/cooperative stochasticdifferential game model to prove that the optimal strategies trajectory ofagents in a system with a topological configuration of a Multi-Local-Worldgraph would converge into a certain attractor if the system’s configuration isfixed. Due to the economics and management property, almost all systems aredivided into several independent Local-Worlds, and the interaction betweenagents in the system is more complex. The interaction between agents inthe same Local-World is defined as a stochastic differential cooperativegame;conversely, the interaction between agents in different Local-Worldsis defined as a stochastic differential non-cooperative game. We construct anon-cooperative/cooperative stochastic differential game model to describethe interaction between agents. The solutions of the cooperative and noncooperativegames are obtained by invoking corresponding theories, and thena nonlinear operator is constructed to couple these two solutions together.At last, the optimal strategies trajectory of agents in the system is proven toconverge into a certain attractor, which means that strategies trajectory arecertainty as time tends to infinity or a large positive integer. It is concluded thatthe optimal strategy trajectory with a nonlinear operator of cooperative/noncooperativestochastic differential game between agents can make agentsin a certain Local-World coordinate and make the Local-World paymentmaximize, and can make the all Local-Worlds equilibrated;furthermore, theoptimal strategy of the coupled game can converge into a particular attractorthat decides the optimal property.展开更多
基金This work is supported by the National Natural Science Foundation (Grant No.10371067)the Youth Teacher Foundation of Fok Ying Tung Education Foundation, the Excellent Young Teachers Program and the Doctoral Program Foundation of MOE and Shandong Province, China.
文摘In this paper, we use the solutions of forward-backward stochastic differential equations to get the explicit form of the optimal control for linear quadratic stochastic optimal control problem and the open-loop Nash equilibrium point for nonzero sum differential games problem. We also discuss the solvability of the generalized Riccati equation system and give the linear feedback regulator for the optimal control problem using the solution of this kind of Riccati equation system.
基金国家自然科学基金，Outstanding Young Teachers of Ministry of Education of China，Special Fund for Ph.D.Program of Ministry of Education of China，Fok Ying Tung Education Foundation
文摘The existence and uniqueness of the solutions for one kind of forward- backward stochastic differential equations with Brownian motion and Poisson process as the noise source were given under the monotone conditions. Then these results were applied to nonzero-sum differential games with random jumps to get the explicit form of the open-loop Nash equilibrium point by the solution of the forward-backward stochastic differential equations.
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.
基金This work was supported by National Key Research&Development Program of China under Grant No.2022YFA1006104National Natural Science Foundations of China under Grant Nos.11971266,11831010Shandong Provincial Natural Science Foundations under Grant Nos.ZR2022JQ01,ZR2020ZD24,ZR2019ZD42.
文摘In this paper,a leader-follower stochastic differential game is studied for a linear stochastic differential equation with quadratic cost functionals.The coefficients in the state equation and the weighting matrices in the cost functionals are all deterministic.Closed-loop strategies are introduced,which require to be independent of initial states;and such a nature makes it very useful and convenient in applications.The follower first solves a stochastic linear quadratic optimal control problem,and his optimal closed-loop strategy is characterized by a Riccati equation,together with an adapted solution to a linear backward stochastic differential equation.Then the leader turns to solve a stochastic linear quadratic optimal control problem of a forward-backward stochastic differential equation,necessary conditions for the existence of the optimal closed-loop strategy for the leader is given by a Riccati equation.Some examples are also given.
基金Project supported by the National Natural Science Foundation of China (No.10371067) thePlanned Item for the Outstanding Young Teachers of Ministry of Education of China (No.2057) the Special Fund for Ph.D. Program of Ministry of Education of China ( No.20020422020) and the Fok Ying Tung Education Foundation for Young College Teachers(No.91064)
文摘The existence and uniqueness of the solutions for one kind of forward-backward stochastic differential equations with Brownian motion and Poisson process as the noise source were given under the monotone conditions.Then these results were applied to nonzero-sum differential games with random jumps to get the explicit form of the open-loop Nash equilibrium point by the solution of the forward-backward stochastic differential equations.
基金supported by the National Natural Science Foundation of China, (Grant Nos.72174064,71671054,and 61976064)the Natural Science Foundation of Shandong Province,“Dynamic Coordination Mechanism of the Fresh Agricultural Produce Supply Chain Driven by Customer Behavior from the Perspective of Quality Loss” (ZR2020MG004)Industrial Internet Security Evaluation Service Project (TC210W09P).
文摘This paper constructs a non-cooperative/cooperative stochasticdifferential game model to prove that the optimal strategies trajectory ofagents in a system with a topological configuration of a Multi-Local-Worldgraph would converge into a certain attractor if the system’s configuration isfixed. Due to the economics and management property, almost all systems aredivided into several independent Local-Worlds, and the interaction betweenagents in the system is more complex. The interaction between agents inthe same Local-World is defined as a stochastic differential cooperativegame;conversely, the interaction between agents in different Local-Worldsis defined as a stochastic differential non-cooperative game. We construct anon-cooperative/cooperative stochastic differential game model to describethe interaction between agents. The solutions of the cooperative and noncooperativegames are obtained by invoking corresponding theories, and thena nonlinear operator is constructed to couple these two solutions together.At last, the optimal strategies trajectory of agents in the system is proven toconverge into a certain attractor, which means that strategies trajectory arecertainty as time tends to infinity or a large positive integer. It is concluded thatthe optimal strategy trajectory with a nonlinear operator of cooperative/noncooperativestochastic differential game between agents can make agentsin a certain Local-World coordinate and make the Local-World paymentmaximize, and can make the all Local-Worlds equilibrated;furthermore, theoptimal strategy of the coupled game can converge into a particular attractorthat decides the optimal property.
