This paper establishes a stochastic maximum principle for a stochastic control of mean-field model which is governed by a Lévy process involving continuous and impulse control.The authors also show the existence ...This paper establishes a stochastic maximum principle for a stochastic control of mean-field model which is governed by a Lévy process involving continuous and impulse control.The authors also show the existence and uniqueness of the solution to a jump-diffusion mean-field stochastic differential equation involving impulse control.As for its application,a mean-variance portfolio selection problem has been solved.展开更多
This paper studies the optimal control of a fully-coupled forward-backward doubly stochastic system driven by Ito-Lévy processes under partial information.The existence and uniqueness of the solution are obtained...This paper studies the optimal control of a fully-coupled forward-backward doubly stochastic system driven by Ito-Lévy processes under partial information.The existence and uniqueness of the solution are obtained for a type of fully-coupled forward-backward doubly stochastic differential equations(FBDSDEs in short).As a necessary condition of the optimal control,the authors get the stochastic maximum principle with the control domain being convex and the control variable being contained in all coefficients.The proposed results are applied to solve the forward-backward doubly stochastic linear quadratic optimal control problem.展开更多
A new class of stochastic processes--Markov skeleton processes is introduced, which have the Markov property on a series of random times. Markov skeleton processes include minimal Q processes, Doob processes, Q proces...A new class of stochastic processes--Markov skeleton processes is introduced, which have the Markov property on a series of random times. Markov skeleton processes include minimal Q processes, Doob processes, Q processes of order one, semi-Markov processes , piecewise determinate Markov processes , and the input processes, the queuing lengths and the waiting times of the system GI/G/1, as particular cases. First, the forward and backward equations are given, which are the criteria for the regularity and the formulas to compute the multidimensional distributions of the Markov skeleton processes. Then, three important cases of the Markov skeleton processes are studied: the (H, G, Π)-processes, piecewise determinate Markov skeleton processes and Markov skeleton processes of Markov type. Finally, a vast vistas for the application of the Markov skeleton processes is presented.展开更多
基金supported in part by the National Nature Science Foundation of China(Nos.12071487,11461032 and 11401267)the Program of Qingjiang Excellent Young Talents,Jiangxi University of Science and Technology,the Science Foundation of Jiangxi Provincial Education Department(No.GJJ190461)the Key R&D plans of Jiangxi Province(No.20202BBEL53006)。
基金supported by the National Science Foundation of China under Grant No.11671404the Fundamental Research Funds for the Central Universities of Central South University under Grant No.10553320171635.
文摘This paper establishes a stochastic maximum principle for a stochastic control of mean-field model which is governed by a Lévy process involving continuous and impulse control.The authors also show the existence and uniqueness of the solution to a jump-diffusion mean-field stochastic differential equation involving impulse control.As for its application,a mean-variance portfolio selection problem has been solved.
基金supported by the Cultivation Program of Distinguished Young Scholars of Shandong University under Grant No.2017JQ06the National Natural Science Foundation of China under Grant Nos.11671404,11371374,61821004,61633015the Provincial Natural Science Foundation of Hunan under Grant No.2017JJ3405
文摘This paper studies the optimal control of a fully-coupled forward-backward doubly stochastic system driven by Ito-Lévy processes under partial information.The existence and uniqueness of the solution are obtained for a type of fully-coupled forward-backward doubly stochastic differential equations(FBDSDEs in short).As a necessary condition of the optimal control,the authors get the stochastic maximum principle with the control domain being convex and the control variable being contained in all coefficients.The proposed results are applied to solve the forward-backward doubly stochastic linear quadratic optimal control problem.
文摘A new class of stochastic processes--Markov skeleton processes is introduced, which have the Markov property on a series of random times. Markov skeleton processes include minimal Q processes, Doob processes, Q processes of order one, semi-Markov processes , piecewise determinate Markov processes , and the input processes, the queuing lengths and the waiting times of the system GI/G/1, as particular cases. First, the forward and backward equations are given, which are the criteria for the regularity and the formulas to compute the multidimensional distributions of the Markov skeleton processes. Then, three important cases of the Markov skeleton processes are studied: the (H, G, Π)-processes, piecewise determinate Markov skeleton processes and Markov skeleton processes of Markov type. Finally, a vast vistas for the application of the Markov skeleton processes is presented.
