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Bilateral Estimation of the Bellman Function in the Problems of Optimal Stochastic Control of Discrete Systems by the Probabilistic Performance Criterion

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Abstract

Consideration was given to the optimal control of discrete stochastic systems by the probabilistic quality criterion. The new characteristics of the Bellman equation for this class of problems were examined, and the two-sided estimate of the Bellman function was determined. The problem of optimal control of the security portfolio with one riskless and a given number of risk assets was considered by way of example. The class of strategies featuring asymptotic optimality was established using the two-sided estimate of the Bellman function.

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Authors and Affiliations

  1. Moscow Aviation Institute (National State University), Moscow, Russia

    V. M. Azanov & Yu. S. Kan

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  1. V. M. Azanov
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  2. Yu. S. Kan
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Correspondence to V. M. Azanov.

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Original Russian Text © V.M. Azanov, Yu.S. Kan, 2018, published in Avtomatika i Telemekhanika, 2018, No. 2, pp. 3–18.

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Azanov, V.M., Kan, Y.S. Bilateral Estimation of the Bellman Function in the Problems of Optimal Stochastic Control of Discrete Systems by the Probabilistic Performance Criterion. Autom Remote Control 79, 203–215 (2018). https://doi.org/10.1134/S0005117918020017

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  • DOI: https://doi.org/10.1134/S0005117918020017

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