Articles

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

  • Chen FEI ,
  • Weiyin FEI
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  • School of Mathematics and Physics, Anhui Polytechnic University, Wuhu 241000, China

Received date: 2013-10-31

  Revised date: 2014-05-11

  Online published: 2015-03-20

Supported by

Project supported by National Natural Science Foundation of China (71171003), Anhui Natural Science Foundation (10040606003), and Anhui Natural Science Foundation of Universities (KJ2012B019, KJ2013B023).

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.

Cite this article

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 . DOI: 10.1016/S0252-9602(15)60014-5

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