A new class of impulse stochastic control models with non-negative control quantity  

作　　者：LIU XiaoPeng LIU KunHui 

机构地区：[1]College of Science, Beijing Jiaotong University, Beijing 100044, China

出　　处：《Science China(Information Sciences)》2011年第3期638-652,共15页中国科学（信息科学）（英文版）

基　　金：supported by the National Natural Science Foundation of China (Grant No. 19671004)

摘　　要：This paper advances and studies a new class of impulse stochastic control models. Its state structure is defined by a linear stochastic differential equation of the semi-martingale, its control cost function is a twovariable function of pre-control state quantity and control quantity, and its control quantity is kept non-negative. First this paper constructs a new type of variational equations and proves its solution exists. Using a series of stochastic analysis methods to research the solution function of this type of variational equations, this paper proves the existence of optimal control and analyzes its structure in depth. Because of the big difference between the model in this paper and stochastic control models in previous papers, the analysis method here is quite different from previous ones. It is expected that this paper will have important theoretical significance for stochastic control research, along with wide applicative value in finance control and security management.

关 键 词：impulse stochastic control control quantity variational equation optimal control semi-martingale 

分 类 号：O231.3[理学—运筹学与控制论] O232[理学—数学]