This paper investigates Nash games for a class of linear stochastic systems governed by Itô’s differential equation with Markovian jump parameters both in finite-time horizon and infinite-time horizon.First,stoc...This paper investigates Nash games for a class of linear stochastic systems governed by Itô’s differential equation with Markovian jump parameters both in finite-time horizon and infinite-time horizon.First,stochastic Nash games are formulated by applying the results of indefinite stochastic linear quadratic(LQ)control problems.Second,in order to obtain Nash equilibrium strategies,crosscoupled stochastic Riccati differential(algebraic)equations(CSRDEs and CSRAEs)are derived.Moreover,in order to demonstrate the validity of the obtained results,stochastic H2/H∞control with state-and control-dependent noise is discussed as an immediate application.Finally,a numerical example is provided.展开更多
In this work we introduce a new unconditionally convergent explicit Tree-Grid Method for solving stochastic control problems with one space and one time dimension or equivalently,the corresponding Hamilton-Jacobi-Bell...In this work we introduce a new unconditionally convergent explicit Tree-Grid Method for solving stochastic control problems with one space and one time dimension or equivalently,the corresponding Hamilton-Jacobi-Bellman equation.We prove the convergence of the method and outline the relationships to other numerical methods.The case of vanishing diffusion is treated by introducing an artificial diffusion term.We illustrate the superiority of our method to the standardly used implicit finite difference method on two numerical examples from finance.展开更多
基金supported by the National Natural Science Foundation of China(No.71171061)China Postdoctoral Science Foundation(No.2014M552177)+2 种基金the Natural Science Foundation of Guangdong Province(No.S2011010004970)the Doctors Start-up Project of Guangdong University of Technology(No.13ZS0031)the 2014 Guangzhou Philosophy and Social Science Project(No.14Q21).
文摘This paper investigates Nash games for a class of linear stochastic systems governed by Itô’s differential equation with Markovian jump parameters both in finite-time horizon and infinite-time horizon.First,stochastic Nash games are formulated by applying the results of indefinite stochastic linear quadratic(LQ)control problems.Second,in order to obtain Nash equilibrium strategies,crosscoupled stochastic Riccati differential(algebraic)equations(CSRDEs and CSRAEs)are derived.Moreover,in order to demonstrate the validity of the obtained results,stochastic H2/H∞control with state-and control-dependent noise is discussed as an immediate application.Finally,a numerical example is provided.
基金supported by the European Union in the FP7-PEOPLE-2012-ITN Program under Grant Agreement Number 304617(FP7 Marie Curie Action,Project Multi-ITN STRIKE-Novel Methods in Computational Finance).
文摘In this work we introduce a new unconditionally convergent explicit Tree-Grid Method for solving stochastic control problems with one space and one time dimension or equivalently,the corresponding Hamilton-Jacobi-Bellman equation.We prove the convergence of the method and outline the relationships to other numerical methods.The case of vanishing diffusion is treated by introducing an artificial diffusion term.We illustrate the superiority of our method to the standardly used implicit finite difference method on two numerical examples from finance.
