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

doi:10.1016/S0252-9602(15)60014-5

Abstract

Abstract:

This article is concerned with a class of control systems with Markovian switching, in which an Itô 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.

Key words: Markov optimal control, generalized Itô, formula, HJB equations, optimal portfolio, three fund theorem, inflation

CLC Number:

93E20

Chen FEI, Weiyin FEI. OPTIMAL CONTROL OF MARKOVIAN SWITCHING SYSTEMS WITH APPLICATIONS TO PORTFOLIO DECISIONS UNDER INFLATION[J].Acta mathematica scientia,Series B, 2015, 35(2): 439-458.

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