Cybernetics and Systems Analysis

, Volume 54, Issue 2, pp 212–220 | Cite as

Dynamic Risk Control in Multidimensional Markov Models

Article

Abstract

The authors consider a typical model used in many fields of applied mathematics regarding selection of optimal decisions in stochastic systems. The multidimensional death process controlled on an interval of random length, which is analyzed in the paper, can be used to describe phenomena that appear in economical, biological, medical, engineering, and other applications. Several approaches are proposed to determine the optimality criteria, the properties of corresponding risk function are investigated, and a computing algorithm is developed for construction of optimal stationary strategies.

Keywords

optimal stationary strategies controlled processes Markov decision-making processes risk function birth-death processes iterative algorithms 

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References

  1. 1.
    A. O. Voyna, “Choosing optimal strategies in stochastic marketing models,” Dopov. Nac. Akad. Nauk Ukr., No. 8, 60–64 (2002).Google Scholar
  2. 2.
    A. A. Voina, “Optimal dynamic strategies for stochastic models of marketing promotion mix,” Cybern. Syst. Analysis, Vol. 40, No. 2, 270–276 (2004).MathSciNetCrossRefMATHGoogle Scholar
  3. 3.
    A. O. Voyna, “Stochastic mathematical models and risk function in constructing optimal marketing strategies,” Zhurn. Obch. Prykl. Matem., No. 89, Issue 2, 2–5 (2004).Google Scholar
  4. 4.
    A. A. Voina and A. Klodzinska, “Risk functions in multidimensional stock control models that function in a random Markov environment,” Cybern. Syst. Analysis, Vol. 40, No. 4, 594–598 (2004).CrossRefMATHGoogle Scholar
  5. 5.
    O. A. Voina, “Risk control in multidimensional insurance models,” Zhurn. Obch. Prykl. Matem., No. 95, Issue 2, 13–23 (2007).Google Scholar
  6. 6.
    A. Wojna, “Ryzyko w procesach finansowych oraz metody badań koniunktury,” Politechnika Koszalińska, Poland (2009).Google Scholar
  7. 7.
    I. I. Gikhman and A. V. Skorokhod, Controlled Random Processes [in Russian], Naukova Dumka, Kyiv (1977).MATHGoogle Scholar
  8. 8.
    Hisashi Mine and Shunji Osaki, Markovian Decision Processes, American Elsevier Pub. Co. (1970).Google Scholar

Copyright information

© Springer Science+Business Media, LLC, part of Springer Nature 2018

Authors and Affiliations

  1. 1.Koszalin University of TechnologyKoszalinPoland
  2. 2.PJSC ProminvestbankKyivUkraine

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