Risk sensitive control of finite state Markov chains in discrete time, with applications to portfolio management. (English) Zbl 0959.91029

Bielecki, Tomasz; Hernández-Hernández, Daniel; Pliska, Stanley R.

Math. Methods Oper. Res. 50, No. 2, 167-188 (1999).

This paper extends standard dynamic programming results for the risk sensitive control of discrete time Markov chains to a new class of models. The state space is only finite, but the assumptions about the Markov transition matrix are less restrictive. The results are applied to the financial problem of managing a portfolio of assets. These are affected by Markovian factors and the investor maximizing the portfolio’s risk adjusted growth rate.
This paper is organized in 6 sections. After the introduction (section 1), the optimal risk sensitive control of finite state Markov chains is described in section 2. In section 3, the discrete time risk sensitive optimal portfolio problem is formulated. In section 4, the theory of section 2 is applied to obtain various fundamental results for the financial application. Numerical examples are regarded in section 5. Finally, concluding remarks follow in section 6.

Reviewer: Klaus Ehemann (Karlsruhe)

MSC:

91B28	Finance etc. (MSC2000)
90C40	Markov and semi-Markov decision processes

Keywords:

risk sensitive Markov decision processes; portfolio optimization; factor modelling