This paper studies the problem of partially observed optimal control for forward-backward stochastic systems which are driven both by Brownian motions and an independent Poisson random measure. Combining forward-backw...This paper studies the problem of partially observed optimal control for forward-backward stochastic systems which are driven both by Brownian motions and an independent Poisson random measure. Combining forward-backward stochastic differential equation theory with certain classical convex variational techniques, the necessary maximum principle is proved for the partially observed optimal control, where the control domain is a nonempty convex set. Under certain convexity assumptions, the author also gives the sufficient conditions of an optimal control for the aforementioned optimal optimal problem. To illustrate the theoretical result, the author also works out an example of partial information linear-quadratic optimal control, and finds an explicit expression of the corresponding optimal control by applying the necessary and sufficient maximum principle.展开更多
This paper is concerned with optimal control of neutral stochastic functional differential equations(NSFDEs). The Pontryagin maximum principle is proved for optimal control, where the adjoint equation is a linear neut...This paper is concerned with optimal control of neutral stochastic functional differential equations(NSFDEs). The Pontryagin maximum principle is proved for optimal control, where the adjoint equation is a linear neutral backward stochastic functional equation of Volterra type(VNBSFE). The existence and uniqueness of the solution are proved for the general nonlinear VNBSFEs. Under the convexity assumption of the Hamiltonian function, a sufficient condition for the optimality is addressed as well.展开更多
This paper considers a firm that sells a durable product with a given market potential.The purpose of the firm is to maximize its profit by determining how much capacity to install before the sales horizon, how many p...This paper considers a firm that sells a durable product with a given market potential.The purpose of the firm is to maximize its profit by determining how much capacity to install before the sales horizon, how many products to produce in accordance with the capacity, and how many products to sell by pricing. Appealing to Pontryagin maximum principle in control theory, the authors obtain the closed-forms of all optimal decisions the firm should make. Furthermore, the optimal production rate and optimal sales rate are both equal to the demand rate, which is caused by the optimal pricing policy during the whole horizon, and the optimal pricing path is increasing with the cost of installing a unit of capacity. Furthermore, numerical analysis reveals the visual impression of the relationship of the parameters.展开更多
This paper considers a stochastic optimal control problem of a forward-backward system with regular-singular controls where the set of regular controls is not necessarily convex and the regular control enters the diff...This paper considers a stochastic optimal control problem of a forward-backward system with regular-singular controls where the set of regular controls is not necessarily convex and the regular control enters the diffusion coefficient.This control problem is difficult to solve with the classical method of spike variation.The authors use the approach of relaxed controls to establish maximum principle for this stochastic optimal control problem.Sufficient optimality conditions are also investigated.展开更多
In this paper,the authors consider a stochastic control problem where the system is governed by a general backward stochastic differential equation.The control domain need not be convex,and the diffusion coefficient c...In this paper,the authors consider a stochastic control problem where the system is governed by a general backward stochastic differential equation.The control domain need not be convex,and the diffusion coefficient can contain a control variable.The authors obtain a stochastic maximum principle for the optimal control of this problem by virtue of the second-order duality method.展开更多
The purpose of this paper is to derive some pointwise second-order necessary conditions for stochastic optimal controls in the general case that the control variable enters into both the drift and the diffusion terms....The purpose of this paper is to derive some pointwise second-order necessary conditions for stochastic optimal controls in the general case that the control variable enters into both the drift and the diffusion terms.When the control region is convex, a pointwise second-order necessary condition for stochastic singular optimal controls in the classical sense is established; while when the control region is allowed to be nonconvex, we obtain a pointwise second-order necessary condition for stochastic singular optimal controls in the sense of Pontryagin-type maximum principle. It is found that, quite different from the first-order necessary conditions,the correction part of the solution to the second-order adjoint equation appears in the pointwise second-order necessary conditions whenever the diffusion term depends on the control variable, even if the control region is convex.展开更多
In this paper,we consider an optimal control problem with state constraints,where the control system is described by a mean-field forward-backward stochastic differential equation(MFFBSDE,for short)and the admissible ...In this paper,we consider an optimal control problem with state constraints,where the control system is described by a mean-field forward-backward stochastic differential equation(MFFBSDE,for short)and the admissible control is mean-field type.Making full use of the backward stochastic differential equation theory,we transform the original control system into an equivalent backward form,i.e.,the equations in the control system are all backward.In addition,Ekeland's variational principle helps us deal with the state constraints so that we get a stochastic maximum principle which characterizes the necessary condition of the optimal control.We also study a stochastic linear quadratic control problem with state constraints.展开更多
Considering the uncertainty of kelp-abalone-sea cucumber population, an interval model of carbon sink fisheries with multi-trophic levels is proposed. The equilibria of the model are identified and the corresponding s...Considering the uncertainty of kelp-abalone-sea cucumber population, an interval model of carbon sink fisheries with multi-trophic levels is proposed. The equilibria of the model are identified and the corresponding stabilities are discussed. And the existence of bionomic equilibrium of the model is investigated. Next the optimal controller is designed to obtain the optimal harvest using Pontryagin's maximum principle. Numerical simulations are carried to prove the results.展开更多
基金This research is supported by the National Nature Science Foundation of China under Grant Nos 11001156, 11071144, the Nature Science Foundation of Shandong Province (ZR2009AQ017), and Independent Innovation Foundation of Shandong University (IIFSDU), China.
文摘This paper studies the problem of partially observed optimal control for forward-backward stochastic systems which are driven both by Brownian motions and an independent Poisson random measure. Combining forward-backward stochastic differential equation theory with certain classical convex variational techniques, the necessary maximum principle is proved for the partially observed optimal control, where the control domain is a nonempty convex set. Under certain convexity assumptions, the author also gives the sufficient conditions of an optimal control for the aforementioned optimal optimal problem. To illustrate the theoretical result, the author also works out an example of partial information linear-quadratic optimal control, and finds an explicit expression of the corresponding optimal control by applying the necessary and sufficient maximum principle.
文摘This paper is concerned with optimal control of neutral stochastic functional differential equations(NSFDEs). The Pontryagin maximum principle is proved for optimal control, where the adjoint equation is a linear neutral backward stochastic functional equation of Volterra type(VNBSFE). The existence and uniqueness of the solution are proved for the general nonlinear VNBSFEs. Under the convexity assumption of the Hamiltonian function, a sufficient condition for the optimality is addressed as well.
基金supported by the National Natural Science Foundation of China under Grant Nos.71201027,71272085,71390334,and 11271356973 Project under Grant No.2010CB731400+3 种基金Humanity and Social Science Youth Foundation of Ministry of Education of China under Grant No.12YJC630260Guangdong Natural Science Foundation under Grant No.S2012040007919Foundation for Distinguished Young Talents in Higher Education of Guangdong under Grant No.LYM11121the Open Fund of Chongqing Key Laboratory of Logistics under Grant No.CQKLL12003
文摘This paper considers a firm that sells a durable product with a given market potential.The purpose of the firm is to maximize its profit by determining how much capacity to install before the sales horizon, how many products to produce in accordance with the capacity, and how many products to sell by pricing. Appealing to Pontryagin maximum principle in control theory, the authors obtain the closed-forms of all optimal decisions the firm should make. Furthermore, the optimal production rate and optimal sales rate are both equal to the demand rate, which is caused by the optimal pricing policy during the whole horizon, and the optimal pricing path is increasing with the cost of installing a unit of capacity. Furthermore, numerical analysis reveals the visual impression of the relationship of the parameters.
基金supported by the National Natural Science Foundation of China under Grant Nos.11201268and 61105077the Natural Science Foundation of Shandong Province under Grant Nos.ZR2011AQ018 andZR2012AQ013
文摘This paper considers a stochastic optimal control problem of a forward-backward system with regular-singular controls where the set of regular controls is not necessarily convex and the regular control enters the diffusion coefficient.This control problem is difficult to solve with the classical method of spike variation.The authors use the approach of relaxed controls to establish maximum principle for this stochastic optimal control problem.Sufficient optimality conditions are also investigated.
文摘In this paper,the authors consider a stochastic control problem where the system is governed by a general backward stochastic differential equation.The control domain need not be convex,and the diffusion coefficient can contain a control variable.The authors obtain a stochastic maximum principle for the optimal control of this problem by virtue of the second-order duality method.
基金supported by the National Basic Research Program of China(973 Program)(Grant No.2011CB808002)National Natural Science Foundation of China(Grant Nos.11221101+4 种基金1123100711401404 and 11471231)the Program for Changjiang Scholars and Innovative Research Team in University(Grant No.IRT1273)the Changjiang Scholars Program from the Chinese Education Ministrythe Spanish Science and Innovation Ministry(Grant No.MTM2011-29306)
文摘The purpose of this paper is to derive some pointwise second-order necessary conditions for stochastic optimal controls in the general case that the control variable enters into both the drift and the diffusion terms.When the control region is convex, a pointwise second-order necessary condition for stochastic singular optimal controls in the classical sense is established; while when the control region is allowed to be nonconvex, we obtain a pointwise second-order necessary condition for stochastic singular optimal controls in the sense of Pontryagin-type maximum principle. It is found that, quite different from the first-order necessary conditions,the correction part of the solution to the second-order adjoint equation appears in the pointwise second-order necessary conditions whenever the diffusion term depends on the control variable, even if the control region is convex.
基金supported by National Natural Science Foundation of China(Grant No.11401091)Postdoctoral Scientific Research Project of Jilin Province(Grant No.RB201357)+2 种基金the Fundamental Research Funds for the Central Universities(Grant No.14QNJJ002)China Postdoctoral Science Foundation(Grant No.2014M551152)the China Scholarship Council
文摘In this paper,we consider an optimal control problem with state constraints,where the control system is described by a mean-field forward-backward stochastic differential equation(MFFBSDE,for short)and the admissible control is mean-field type.Making full use of the backward stochastic differential equation theory,we transform the original control system into an equivalent backward form,i.e.,the equations in the control system are all backward.In addition,Ekeland's variational principle helps us deal with the state constraints so that we get a stochastic maximum principle which characterizes the necessary condition of the optimal control.We also study a stochastic linear quadratic control problem with state constraints.
文摘Considering the uncertainty of kelp-abalone-sea cucumber population, an interval model of carbon sink fisheries with multi-trophic levels is proposed. The equilibria of the model are identified and the corresponding stabilities are discussed. And the existence of bionomic equilibrium of the model is investigated. Next the optimal controller is designed to obtain the optimal harvest using Pontryagin's maximum principle. Numerical simulations are carried to prove the results.