Model of Stabilizing of the Interest Rate on Deposits Banking System Using by Moment Equations

Dzhalladova, Irada; Michalková, Mária; Růžičková, Miroslava

doi:10.2478/tmmp-2013-0004

Abstract

The paper deals with a system of difference equations, where coefficients depend on Markov chains. The functional equations for particular density and the moment equations for the system are derived and used in the investigation of solvability and stability. An application of the results is shown how to solve various economic problems.

References

[1] ANISIMOV, V. V.: Random Processes with Discrete Components. Vyshcha shkola, Kiev, 1988. (In Russian)
Search in Google Scholar
[2] ÅSTRÖM, K. J.: Introduction to Stochastic Control Theory. Academic Press, New York, 1970.
Search in Google Scholar
[3] BARBASHYN, E. A.: Lyapunov Functions. Nauka, Moscow, 1970. (In Russian)
Search in Google Scholar
[4] DZHALLADOVA, I. A.: Optimization of Stochastic System. KNEU, Kiev, 2005. (In Russian)
Search in Google Scholar
[5] FELMER, G.-SHID, A.: Vvedenie v Stokhasticheskie Finansy. Diskretnoe Vremja. MTsMNO, Moscow, 2008. (In Russian)
Search in Google Scholar
[6] GIHMAN,I. I.-SKOROHOD, A. V.: Controlled Stochastic Processes. Springer-Verlag, New York, 1979.10.1007/978-1-4612-6202-2
Search in Google Scholar
[7] HASMINSKI, R. Z.: Stochastic Stability of Differential Equations. Sijthoff & Noordhoff, Alphen aan den Rijn, 1980.
Search in Google Scholar
[8] HRISANOV, S. M.: Moment systems group, Ukrainian Math. J. 33 (1981), 787-792. (In Russian)
Search in Google Scholar
[9] IKEDA, N.-WATANABE, S.: Stochastic Differential Equations and Diffusion Processes. North Holland, Amsterdam, 1989.
Search in Google Scholar
[10] JACOD, J.-SHIRYAEV, A. N.: Limit Theorems for Stochastic Processes. Springer-Verlag, New York, 1987.10.1007/978-3-662-02514-7
Search in Google Scholar
[11] JASINSKIY, V. K.-JASINSKIY, E. V.: Problem of Stability and Stabilization of DynamicSystems with Finite Aftereffect. TVIMS, Kiev, 2005.
Search in Google Scholar
[12] KATZ, I. YA.: Lyapunov Function Method in Stability and Stabilization Problems forRandom-Structure Systems. Izd. Ural. Gos. Akad., 1998. (In Russian)
Search in Google Scholar
[13] KATZ, I. YA.-KRASOVSKII, N. N.: On stability of systems with random parameters, Prikl. Mat. Mekh. 24 (1960), 809-823. (In Russian)
Search in Google Scholar
[14] KOLMOGOROV, A. N.: Selected Works of A. N. Kolmogorov (Probability Theory andMathematical Statistics). Springer, New York, 1992.
Search in Google Scholar
[15] KOROLYUK, V. S.-LIMNIOS, W.: Stochastic Systems in Merging Phase Space. Word Scientific, London, 2006.10.1142/5979
Search in Google Scholar
[16] KOROLYUK, V.S.-KOROLYUK,V.V.: Stochastic Models of Systems. Naukova Dumka, Kiev, 1989. (In Russian)
Search in Google Scholar
[17] KORENIVSKYI, D. H.: The Destabilizing Effect of ParametricWhite Noise in Continuousand Discrete Dynamical Systems. Akademperiodika, Kiev, 2008. (In Russian)
Search in Google Scholar
[18] KOROLYUK, V. S.: Semi-Markov Processes and their Applications. Naukova Dumka, Kiev, 1976. (In Russian)
Search in Google Scholar
[19] LEVI, P.: Stochastic Processes and Brownian Motion. Nauka, Moscow, 1972. (In Russian)
Search in Google Scholar
[20] LYAPUNOV, A. M.: General Problem of the Stability of Motion. Tayor & Francis, London, 1992.10.1080/00207179208934253
Search in Google Scholar
[21] OKSENDAL, B.: Stochastic Differential Equations. Springer-Verlag, Berlin, 2000.
Search in Google Scholar
[22] PUGACHEV, V. S.: Stochastic Systems: Theory and Applications.World Scientific Publ., River Edge, NJ, 2001.10.1142/4805
Search in Google Scholar
[23] SAMOILENKO, A. M.-PERESTYUK, N. A.: Impulsive Differential Equations. Vyshcha Shkola, Kiev, 1987. (In Russian)
Search in Google Scholar
[24] SVESHNIKOV, A. A.: Applied Methods of the Theory of Random Functions. Pergamon Press, Oxford, 1966.10.1016/B978-1-4831-9760-9.50009-1
Search in Google Scholar
[25] TIKHONOV, V. I.-MIRONOV, M. A.: Markov Processes. Sovetskoe Radio, Moscow, 1977. (In Russian)
Search in Google Scholar
[26] VALEEV, K. G.-DZHALLADOVA, I. A.: Optimization of Random Process. KNEU, Kiev, 2006. (In Russian)
Search in Google Scholar
[27] ZUBOV, V. I.: Methods of A. M. Lyapunov and their Application. P. Noordhoff, Ltd., Groningen, 1964.
Search in Google Scholar

Model of Stabilizing of the Interest Rate on Deposits Banking System Using by Moment Equations

Abstract

Paradigm

My account