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Reduction of the two-step problem of stochastic optimal control with bilinear model to the problem of mixed integer linear programming

  • Stochastic Systems, Queueing Systems
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Abstract

Consideration was given to the two-step problem of stochastic optimization with a bilinear model which describes the problem of forming the securities portfolio consisting of some risk assets and one riskless asset. The probability of exceeding the given threshold of capital is used as the optimality criterion. At the second step, the piecewise constant control is used as the capital control. Determined were the upper and lower estimates of the probability functional. The problems of maximizing the upper and lower estimates of the probability functional were reduced to the problems of mixed integer linear programming by means of discretizing the probabilistic measure. An algorithm to seek an approximate solution to the original problem was proposed, and an example was considered.

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Authors and Affiliations

  1. Moscow State Aviation Institute, Moscow, Russia

    A. I. Kibzun & A. N. Ignatov

Authors
  1. A. I. Kibzun
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  2. A. N. Ignatov
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Correspondence to A. I. Kibzun.

Additional information

Original Russian Text © A.I. Kibzun, A.N. Ignatov, 2016, published in Avtomatika i Telemekhanika, 2016, No. 12, pp. 89–111.

This paper was recommended for publication by P.S. Shcherbakov, a member of the Editorial Board

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Kibzun, A.I., Ignatov, A.N. Reduction of the two-step problem of stochastic optimal control with bilinear model to the problem of mixed integer linear programming. Autom Remote Control 77, 2175–2192 (2016). https://doi.org/10.1134/S0005117916120079

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  • DOI: https://doi.org/10.1134/S0005117916120079

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