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Asymptotic optimization for stochastic models based on a compound poisson process

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Abstract

This paper considers the possibility of using a multidimensional compound Poisson process controlled by a continuous-time Markov chain in mathematical decision-making models. A definition of this process is presented and examples are given that illustrate its use in formalizing the concepts of “uncertainty” and “risk” and constructing risk functions and objective functions for the corresponding optimization problems. Some approaches are proposed to solve these problems, in particular, a direct analytic approach consisting of finding explicit formulas for a risk function and a method of approximate solution based on limit theorems of stochastic process theory.

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Authors and Affiliations

  1. Koszalin University of Technology “Politechnika Koszalinska”, Koszalin, Poland

    A. A. Voina

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  1. A. A. Voina
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Correspondence to A. A. Voina.

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Translated from Kibernetika i Sistemnyi Analiz, No. 4, pp. 165–175, July–August 2011.

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Voina, A.A. Asymptotic optimization for stochastic models based on a compound poisson process. Cybern Syst Anal 47, 649–658 (2011). https://doi.org/10.1007/s10559-011-9345-z

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  • DOI: https://doi.org/10.1007/s10559-011-9345-z

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