OPTIMAL CONTROL OF MARKOVIAN SWITCHING SYSTEMS WITH APPLICATIONS TO PORTFOLIO DECISIONS UNDER INFLATION  

作　　者：费晨 费为银 

机构地区：[1]School of Mathematics and Physics,Anhui Polytechnic University

出　　处：《Acta Mathematica Scientia》2015年第2期439-458,共20页数学物理学报（B辑英文版）

基　　金：supported by National Natural Science Foundation of China(71171003);Anhui Natural Science Foundation(10040606003);Anhui Natural Science Foundation of Universities(KJ2012B019,KJ2013B023)

摘　　要：This article is concerned with a class of control systems with Markovian switching, in which an It5 formula for Markov-modulated processes is derived. Moreover, an optimal control law satisfying the generalized Hamilton-Jacobi-Bellman （HJB） equation with Markovian switching is characterized. Then, through the generalized HJB equation, we study an optimal consumption and portfolio problem with the financial markets of Markovian switching and inflation. Thus, we deduce the optimal policies and show that a modified Mutual Fund Theorem consisting of three funds holds. Finally, for the CRRA utility function, we explicitly give the optimal consumption and portfolio policies. Numerical examples are included to illustrate the obtained results.This article is concerned with a class of control systems with Markovian switching, in which an It5 formula for Markov-modulated processes is derived. Moreover, an optimal control law satisfying the generalized Hamilton-Jacobi-Bellman （HJB） equation with Markovian switching is characterized. Then, through the generalized HJB equation, we study an optimal consumption and portfolio problem with the financial markets of Markovian switching and inflation. Thus, we deduce the optimal policies and show that a modified Mutual Fund Theorem consisting of three funds holds. Finally, for the CRRA utility function, we explicitly give the optimal consumption and portfolio policies. Numerical examples are included to illustrate the obtained results.

关 键 词：Markov optimal control generalized It6 formula HJB equations optimal portfolio three fund theorem INFLATION 

分 类 号：O231[理学—运筹学与控制论]