Dynamic Programming for Multidimensional Stochastic Control Problems  

作　　者：Jin Ma Department of Mathematics,Purdue University,West Lafayette,IN 47907-1395,U S A E-mail:[e-mail],eduJiongmin Yong Laboratory of Mathematics for Nonlinear Science,Department of Mathematics,and Institute of Mathematical Finance,Fudan University,Shanghai 200433,P.R.China E-mail:jyong@fudan,edu.cn 

出　　处：《Acta Mathematica Sinica,English Series》1999年第4期485-506,共22页数学学报（英文版）

摘　　要：In this paper we study a general multidimensional diffusion-type stochastic control problem. Our model contains the usual regular control problem,singular control problem and impulse control problem as special cases.Using a unified treatment of dynamic programming,we show that the value function of the problem is a viscosity solution of certain Hamilton-Jacobi-Bellman (HJB) quasi- variational inequality.The uniqueness of such a quasi-variational inequality is proved.In this paper we study a general multidimensional diffusion-type stochastic control problem. Our model contains the usual regular control problem,singular control problem and impulse control problem as special cases.Using a unified treatment of dynamic programming,we show that the value function of the problem is a viscosity solution of certain Hamilton-Jacobi-Bellman (HJB) quasi- variational inequality.The uniqueness of such a quasi-variational inequality is proved.

关 键 词：Stochastic control Dynamic programming Viscosity solutions Singular control Impulse control 

分 类 号：O1[理学—数学]