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Dynamic Programming for a Stochastic Markovian Process with an Application to the Mean Variance Models

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  • Juval Goldwerger

    (Bar-Ilan University)

Abstract

This paper presents a fresh perspective on the Markov reward process. In order to bring Howard's [Howard, R. A. 1969. Dynamic Programing and Markov-Process. The M.I.T. Press, 5th printing.] model closer to practical applicability, two very important aspects of the model are restated: (a) We make the rewards random variables instead of known constants, and (b) we allow for any decision rule over the moment set of the portfolio distribution, rather than assuming maximization of the expected value of the portfolio outcome. These modifications provide a natural setting for the rewards to be normally distributed, and thus, applying the mean variance models becomes possible. An algorithm for solution is presented, and a special case: the mean-variability models decision rule of maximizing (\mu /\sigma) is worked out in detail.

Suggested Citation

  • Juval Goldwerger, 1977. "Dynamic Programming for a Stochastic Markovian Process with an Application to the Mean Variance Models," Management Science, INFORMS, vol. 23(6), pages 612-620, February.
    • Handle: RePEc:inm:ormnsc:v:23:y:1977:i:6:p:612-620
    DOI: 10.1287/mnsc.23.6.612
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    Cited by:

    1. Jan Kaluski, 2000. "An Analytical Method To Calculate The Ergodic And Difference Matrices Of The Discounted Markov Decision Processes," Computing in Economics and Finance 2000 235, Society for Computational Economics.

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