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 Hamilt...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.展开更多
基金supported by National Natural Science Foundation of China(71171003)Anhui Natural Science Foundation(10040606003)Anhui Natural Science Foundation of Universities(KJ2012B019,KJ2013B023)
文摘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.
