Risk sensitive control of finite state Markov chains in discrete time, with applications to portfolio management

Abstract. In this paper we extend standard dynamic programming results for the risk sensitive optimal control of discrete time Markov chains to a new class of models. The state space is only finite, but now the assumptions about the Markov transition matrix are much less restrictive. Our results are then applied to the financial problem of managing a portfolio of assets which are affected by Markovian microeconomic and macroeconomic factors and where the investor seeks to maximize the portfolio's risk adjusted growth rate.

[1]  S. Pliska,et al.  Risk sensitive asset allocation , 2000 .

[2]  A. Bensoussan,et al.  On Bellman equations of ergodic control in n. , 1992 .

[3]  S. Rachev,et al.  Modeling asset returns with alternative stable distributions , 1993 .

[4]  W. Fleming,et al.  Risk sensitive control of finite state machines on an infinite horizon. I , 1997, Proceedings of the 36th IEEE Conference on Decision and Control.

[5]  A. Timmermann,et al.  Predictability of Stock Returns: Robustness and Economic Significance , 1995 .

[6]  S.,et al.  Multiplicative Ergodicityfor an Irreducible Markov Chain , 1999 .

[7]  R. C. Merton,et al.  AN INTERTEMPORAL CAPITAL ASSET PRICING MODEL , 1973 .

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

[9]  Sean P. Meyn,et al.  Risk sensitive dynamic programming with unbounded cost , 1999, Proceedings of the 38th IEEE Conference on Decision and Control (Cat. No.99CH36304).

[10]  S. Marcus,et al.  Risk sensitive control of Markov processes in countable state space , 1996 .

[11]  P. Whittle.  Risk-Sensitive Optimal Control , 1990 .

[12]  A. Bensoussan,et al.  On Bellman equations of ergodic control in Rn , 1992 .

[13]  O. Hernondex-lerma,et al.  Adaptive Markov Control Processes , 1989 .

[14]  Lukasz Stettner,et al.  Risk-Sensitive Control of Discrete-Time Markov Processes with Infinite Horizon , 1999, SIAM J. Control. Optim..

[15]  S. Marcus,et al.  Existence of Risk-Sensitive Optimal Stationary Policies for Controlled Markov Processes , 1999 .

[16]  J. Huston McCulloch,et al.  13 Financial applications of stable distributions , 1996 .

[17]  H. Nagai.  Bellman equations of risk sensitive control , 1995, Proceedings of 1995 34th IEEE Conference on Decision and Control.

[18]  O. Hernández-Lerma.  Adaptive Markov Control Processes , 1989 .