Cybernetics and Systems Analysis

, Volume 55, Issue 5, pp 817–827 | Cite as

Mathematical Models of Risk Control for Regenerating Markov Processes

  • O. A. VoinaEmail author
  • A. O. Voyna


Within the framework of the mathematical model conventionally called “parallel Markov structure,” a number of practical statements of optimal control problems are formalized. The properties of the models and of the random processes used to construct them are examined. In addition, the algorithms to calculate the cost of the corresponding risk functions and to generate optimal control strategies are developed.


regenerating process parallel structure optimal stationary strategies Markov decision processes risk function iterative algorithms 


Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.


  1. 1.
    O. A. Voina and A. O. Voina, “Dynamic risk control in multidimentional Markov models,” Cybern. Syst. Analysis, Vol. 54, No. 2, 212–220 (2018).MathSciNetCrossRefGoogle Scholar
  2. 2.
    I. I. Gikhman and A.V. Skorokhod, Controlled Random Processes [in Russian], Naukova Dumka, Kyiv (1977).zbMATHGoogle Scholar
  3. 3.
    H. Mine and S. Osaki, Markov Decision Processes, Elsevier, New York (1970).zbMATHGoogle Scholar
  4. 4.
    A. Wojna, Ryzyko w procesach finansowych oraz metody badan koniunktury [in Polish], Politechnika Koszalinska (2009).Google Scholar
  5. 5.
    A. O. Voina, “Stochastic mathematical models and risk function in generating optimal Markov strategies,” Zhurn. Obchysl. ta Prykl. Matematyky, Issue 2, No. 89, 2–5 (2004).Google Scholar
  6. 6.
    O. A. Voina, “Optimal regenerating control in Markov models,” Doslidzhennya Operatsii ta ASU, Issue 39, 3–10 (1992).Google Scholar
  7. 7.
    A. A. Voina, “Optimal dynamic strategies for stochastic models of marketing promotion mix,” Cybern. Syst. Analysis, Vol. 40, No. 2, 270–276 (2004).MathSciNetCrossRefGoogle Scholar
  8. 8.
    I. I. Gikhman and A. V. Skorokhod, Theory of Random Processes [in Russian], Nauka, Moscow, Vol. 1 (1971), Vol. 2 (1973).Google Scholar
  9. 9.
    A. A. Voina, “An optimal inventory control model,” Dokl. AN UkrSSR, Ser. A, No. 1, 11–14 (1983).Google Scholar
  10. 10.
    A. O. Voina, “Choosing optimal strategies in stochastic marketing models,” Dopov. Nac. Akad. Nauk Ukr., No. 8, 60–64 (2002).Google Scholar
  11. 11.
    FLOPS. Performance records. Cost of computing. URL:
  12. 12.
    Internet Usage Statistics. World Internet Users and 2018 Population Stats. URL:

Copyright information

© Springer Science+Business Media, LLC, part of Springer Nature 2019

Authors and Affiliations

  1. 1.Taras Shevchenko National University of KyivKyivUkraine
  2. 2.PSC ProminvestbankKyivUkraine

Personalised recommendations