Abstract
A competitive market model with a polyvariant profit function is investigated as applied to the competing banking portfolio medium under conditions of “zeitnot” stock behavior of clients with a view to devising optimal strategies. The method of associated Markov processes is developed with a view to finding an optimal strategy for choosing the most valuable share package for monovariant and bivariant profit functions. Under certain constraints on the so-called bank “promotional” parameter with respect to the “fee” for a missed share package transaction in the case of an asymptotically large portfolio size, universal transcendental equations are obtained that determine the optimal share package choice among competing strategies with monovariant and bivariant profit functions.
This is a preview of subscription content, log in via an institution to check access.
Similar content being viewed by others
References
V. A. Berezovskii and A. V. Gnedin, The Problem of Best Choice [in Russian], Nauka, Moscow (1984).
M. H. A. Davis, V. G. Panas, and T. Zariphopoulou, “European option pricing with transaction costs,” SIAM J. Contr. Optimiz., 31, 470–493 (1993).
M. H. A. Davis and A. R. Norman, “Portfolio selection with transaction costs,” Mathemat. of Oper. Res., 15, 676–713 (1990).
E. L. Presman and I. M. Sonin, “Game problems of optimal stopping: Existence and uniqueness of equilibrium points,” in: Probabilistic Control Problems in Economics, Nauka, Moscow (1977), pp. 115–144.
V. V. Mazalov and S. V. Vinnichenko, Stopping Times and Controlled Random Walks [in Russian], Nauka, Novosibirsk (1992).
W. Feller, An Introduction to Probability Theory and Its Applications [Russian translation], Vol. 1, Mir, Moscow (1984).
C. De Witt Morette and K. D. Elworthy, “A stepping stone in stochastic analysis,” Physics Rep., 77/3, 125–167 (1981).
L. Arnold, “Qualitive theory of stochastic systems and its application in physics,” Physics Rep., 77/3, 215–219 (1981).
J. L. Doob, Probabilistic Processes [Russian translation], IL, Moscow (1956).
R. C. Merton, “Optimization consumption and portfolio rules in a continuous-time model,” J. Econom. Theory, 3, 373–413 (1971).
R. Bellman, Dynamic Programming [Russian translation], IL, Moscow (1960).
J. Gilbert and F. Mosteller, “Recognizing the maximum of a sequence,” J. American Stat. Ass., 61, 35–73 (1966).
A. O. Gel’fond, Finite Differences Theory [in Russian], Gostekhizdat, Moscow (1957).
M. V. Fedoryuk, Asymptotic Methods [in Russian], Nauka, Moscow (1985).
B. Yu. Kyshakevych, A. K. Prykarpats’kyi, and I. P. Tverdokhlib, “Analysis of optimal strategies of a competing stock market model,” Dop. NAN Ukr., No. 1, 40–47 (2009).
B. Yu. Kyshakevych, A. K. Prykarpats’kyi, and I. P. Tverdokhlib, “The study of optimal strategies of a competing stock market model with a bi-variant profit function,” Dop. NAN Ukr., No. 8, 35–41 (2009).
Author information
Authors and Affiliations
Corresponding author
Additional information
Translated from Kibernetika i Sistemnyi Analiz, No. 2, pp. 40–61, March–April 2011.
Rights and permissions
About this article
Cite this article
Kyshakevych, B.Y., Prykarpats’kyi, A.K. & Tverdokhlib, I.P. Analysis of optimal strategies for a competing stock market portfolio model with a polyvariant profit function. Cybern Syst Anal 47, 210–227 (2011). https://doi.org/10.1007/s10559-011-9304-8
Received:
Published:
Issue Date:
DOI: https://doi.org/10.1007/s10559-011-9304-8