Automation and Remote Control

, Volume 62, Issue 9, pp 1489–1501 | Cite as

Optimal Control of the Portfolio

  • A. I. Kibzun
  • E. A. Kuznetsov


Consideration was given to the optimal control of the bilinear system describing the investments in securities of two kinds. The exchange paradox caused by an unsuccessful choice of the optimality criterion in the form of mean income was discussed. One way around this problem is to use the value of the capital guaranteed with a given probability as the optimality criterion. To handle the arising problem, a new strategy of building the portfolio of securities on the basis of the confidence method and sampling of the probabilistic measure was proposed. Its efficiency as compared with the risk and logarithmic strategies was estimated by way of a model example.


Income Mechanical Engineer Probabilistic Measure System Theory Optimality Criterion 
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  1. 1.
    Dupačová, J., Portfolio Optimization via Stochastic Programming: Methods of Output Analysis, Math. Meth. Oper. Res., 1999, vol. 50, pp. 245-270.Google Scholar
  2. 2.
    Szêkely, G.J., Paradoxes in Probability Theory and Mathematical Statistics, Budapest: Akademiai Kiadó, 1986. Translated under the title Paradoksy v teorii veroyatnostei i matematicheskoi statistike, Moscow: Mir, 1990.Google Scholar
  3. 3.
    Kataoka, S., On a Stochastic Programming Model, Econometrica, 1963, vol. 31, pp. 181-196.Google Scholar
  4. 4.
    Moéseke, P., Stochastic Portfolio Programming: The Game Solution, in Stochastic Programming, Dempster, M.A.H., Ed., London: Academic, 1980.Google Scholar
  5. 5.
    Roy, A.D., Safety-first and the Holding of Assets, Econometrica, 1952, vol. 20, pp. 431-449.Google Scholar
  6. 6.
    Kibzun, A.I. and Kan, Yu.S., Stochastic Programming Problems with Probability and Quantile Functions, Chichester: Wiley, 1996.Google Scholar
  7. 7.
    Raik, E., On the Quantile Function in the Problem of Nonlinear Stochastic Programming, Izv. Akad. Nauk Est. SSR, Ser. Fiz.-Tech. Nauk, 1971, vol. 24, no. 1, pp. 3-8.Google Scholar
  8. 8.
    Robbins, H. and Monro, S., A Stochastic Approximation Method, Ann. Math. Statist., 1951, vol. 22, pp. 400-407.Google Scholar
  9. 9.
    Rosenblatt-Roth, M., Quantiles and Medians, Ann. Math. Statist., 1965, vol. 36, pp. 921-925.Google Scholar
  10. 10.
    Bertsekas, D.P., and Sreve, S.E., Stochastic Optimal Control, New York: Academic, 1978. Translated under the title Stokhasticheskoe optimal'noe upravlenie, Moscow: Nauka, 1984.Google Scholar
  11. 11.
    Kibzun, A.I. and Kurbakovskiy, V.Yu., Guaranteeing Approach to Solving Quantile Optimization Problems, Ann. Oper. Res., vol. 30, pp. 81-94.Google Scholar
  12. 12.
    Kelly, J., A New Interpretation of Information Rate, Bell System Tech. J., 1956, vol. 35, pp. 917-926.Google Scholar
  13. 13.
    Kibzun, A.I. and Malyshev, V.V., Optimal Control of the Stochastic Discrete-time System, Izv. Akad. Nauk SSSR, Tekh. Kibern., 1985, no. 6, pp. 113-120.Google Scholar
  14. 14.
    Polyak, B.T., Vvedenie v optimizatsiyu (Introduction to Optimization), Moscow: Nauka, 1983.Google Scholar

Copyright information

© MAIK “Nauka/Interperiodica” 2001

Authors and Affiliations

  • A. I. Kibzun
    • 1
  • E. A. Kuznetsov
    • 1
  1. 1.Moscow State Aviation InstituteMoscowRussia

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