Portfolio Optimization in a Markov Modulated Market ∗

We address a portfolio optimization problem in a Markov modulated market. In this paper both of the terminal expected utility optimization on finite time horizon and risk-sensitive portfolio optimization on finite and infinite time horizon are considered. A numerical procedure is also developed to compute the optimal expected terminal utility for finite horizon problem.

[1]  Charles R. Johnson,et al.  Matrix analysis , 1985, Statistical Inference for Engineers and Data Scientists.

[2]  Thorsten Gerber,et al.  Semigroups Of Linear Operators And Applications To Partial Differential Equations , 2016 .

[3]  Najmeh Salehi,et al.  Risk Sensitive Intertemporal CAPM , 2013 .

[4]  E. Süli,et al.  Numerical Solution of Partial Differential Equations , 2014 .

[5]  Viswanathan Arunachalam,et al.  Introduction to Mathematical Finance , 2012 .

[6]  Nicole Bäuerle,et al.  Portfolio optimization with Markov-modulated stock prices and interest rates , 2004, IEEE Transactions on Automatic Control.

[7]  Gang George Yin,et al.  Markowitz's mean-variance portfolio selection with regime switching: from discrete-time models to their continuous-time limits , 2004, IEEE Transactions on Automatic Control.

[8]  Jakša Cvitanić,et al.  Introduction to the Economics and Mathematics of Financial Markets , 2004 .

[9]  Toshiki Honda,et al.  Optimal portfolio choice for unobservable and regime-switching mean returns , 2003 .

[10]  Gang George Yin,et al.  Markowitz's Mean-Variance Portfolio Selection with Regime Switching: A Continuous-Time Model , 2003, SIAM J. Control. Optim..

[11]  Robert J. Elliott,et al.  American options with regime switching , 2002 .

[12]  Arnaud de La Fortelle,et al.  Large Deviation Principle for Markov Chains in Continuous Time , 2001, Probl. Inf. Transm..

[13]  W. Fleming,et al.  Risk‐Sensitive Control and an Optimal Investment Model , 2000 .

[14]  S. Pliska,et al.  Risk-Sensitive Dynamic Asset Management , 1999 .

[15]  G. Micula,et al.  Numerical Treatment of the Integral Equations , 1999 .

[16]  Wendell H. Fleming,et al.  Risk-Sensitive Production Planning of a Stochastic Manufacturing System , 1998 .

[17]  William M. McEneaney,et al.  Risk-Sensitive and Robust Escape Criteria , 1997 .

[18]  M. Schweizer Approximation pricing and the variance-optimal martingale measure , 1996 .

[19]  W. Fleming,et al.  Risk-Sensitive Control on an Infinite Time Horizon , 1995 .

[20]  Wendell H. Fleming Optimal investment models and risk sensitive stochastic control , 1995 .

[21]  Mario Lefebvre,et al.  Risk-sensitive optimal investment policy , 1994 .

[22]  Hiroshi Konno,et al.  Optimal portfolios with asymptotic criteria , 1993, Ann. Oper. Res..

[23]  W. Fleming,et al.  Controlled Markov processes and viscosity solutions , 1992 .

[24]  D. Duffie,et al.  Mean-variance hedging in continuous time , 1991 .

[25]  R. Kress Linear Integral Equations , 1989 .

[26]  R. Taylor,et al.  The Numerical Treatment of Integral Equations , 1978 .

[27]  David A. H. Jacobs,et al.  The State of the Art in Numerical Analysis. , 1978 .

[28]  S. Varadhan,et al.  Asymptotic evaluation of certain Markov process expectations for large time , 1975 .

[29]  I. I. Gikhman,et al.  The Theory of Stochastic Processes II , 1975 .

[30]  R. C. Merton,et al.  Optimum Consumption and Portfolio Rules in a Continuous-Time Model* , 1975 .

[31]  N. H. Hakansson. MULTI-PERIOD MEAN-VARIANCE ANALYSIS: TOWARD A GENERAL THEORY OF PORTFOLIO CHOICE* , 1971 .

[32]  P. Samuelson LIFETIME PORTFOLIO SELECTION BY DYNAMIC STOCHASTIC PROGRAMMING , 1969 .