数学物理学报(英文版) ›› 2015, Vol. 35 ›› Issue (2): 439-458.doi: 10.1016/S0252-9602(15)60014-5

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

费晨, 费为银   

  1. School of Mathematics and Physics, Anhui Polytechnic University, Wuhu 241000, China
  • 收稿日期:2013-10-31 修回日期:2014-05-11 出版日期:2015-03-20 发布日期:2015-03-20
  • 通讯作者: Weiyin FEI School of Mathematics and Physics, Anhui Polytechnic University, Wuhu 241000, China E-mail: 438014575@qq.com; wyfei@ahpu.edu.cn E-mail:438014575@qq.com;wyfei@ahpu.edu.cn
  • 基金资助:

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

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

Chen FEI, Weiyin FEI   

  1. School of Mathematics and Physics, Anhui Polytechnic University, Wuhu 241000, China
  • Received:2013-10-31 Revised:2014-05-11 Online:2015-03-20 Published:2015-03-20
  • Contact: Weiyin FEI School of Mathematics and Physics, Anhui Polytechnic University, Wuhu 241000, China E-mail: 438014575@qq.com; wyfei@ahpu.edu.cn E-mail:438014575@qq.com;wyfei@ahpu.edu.cn
  • 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).

摘要:

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.

关键词: Markov optimal control, generalized Itô, formula, HJB equations, optimal portfolio, three fund theorem, inflation

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

中图分类号: 

  • 93E20