Two-criteria optimal control problem using Germeier convolution
https://doi.org/10.22405/2226-8383-2018-27-1-51-62
Abstract
Modern mathematical models, computer technologies, financial instruments and mechanisms have formed a new scientific sphere – "financial engineering". In the context of financial engineering, the formulation of new mathematical problems of financial resource management, including the modification of target functionals, is of interest. In this paper, one of the variants of such modification is proposed, namely, for a two-sector model of economic dynamics, a twocriteria problem is considered formalized as a maximin control problem. A complete study of the dependence of the type of optimal trajectory on the value of the control interval is carried out.
About the Authors
Victor Alexandrovich Gorelik
Federal Research Center “Computer Science and Control” of RAS; Moscow State Pedagogical University
Russian Federation
Russian Federation
doctor of physical and mathematical sciences
Tatiana Valerianovna Zolotova
Financial University under the Government of the Russian Federation
Russian Federation
Russian Federation
doctor of physical and mathematical sciences, professor
References
1. Damodaran, A. 2018, Damodaran on valuation: security analysis for investment and corporate finance, John Wiley and Sons, New Jersey, 704 p.
2. Miller, M.H. 1991, Financial innovations and market volatility, Blackwell, Cambridge, MA, 288 p.
3. Moyer, R.C., McGuigan, J.R. & Kretlow, W.J. 2008, Contemporary financial management, South-Western College Pub, Nashville, 880 p.
4. Merton, R.C. 1992, Continuous-time finance, Wiley-Blackwell, New Jersey, 752 p.
5. Petrov, A.A., Pospelov, I.G. & Shananin, A.A. 1992, Experience of mathematical modeling of the economy, Energoatomizdat, Moscow, 544 p.
6. Ashmanov, S.A. 1980, Mathematical models and methods in economics, Moscow University Press, Moscow, 199 p.
7. Gorelik, V.A. 1983, “Maximin problems on connected sets in Banach spaces”, Cybernetics, vol. 19, no. 1, pp. 81–86.
8. Gorelik, V.A. & Tarakanov, A.F. 1992, “Penalty method and maximum principle for nonsmooth variable-structure control problems”, Cybernetics and Systems Analysis, vol. 28, no. 3, pp. 432–437.
9. Dementyev, N.P. 1991, Turnpike properties of models of economic dynamics with consumption, Nauka, Novosibirsk, 167 p.
10. Lotov, A.V. 2021, Introduction to economic and mathematical modeling, 2nd edn, Nauka, Moscow, 400 p.
11. Pospelov, I.G. 2015, “Simplicity of economic complexity: strong main effect”, in Sociophysics and socioengineering: Proceedings of the Conference, Lomonosov Moscow State University, Moscow, pp. 21–22.
12. Trusov, N.V. 2020, “Numerical solution of mean field games problems with turnpike effect”, Lobachevskii Journal of Mathematics, vol. 41, no. 4, pp. 561–576.
13. Zaslavski, A. 2005, Turnpike properties in the calculus of variations and optimal control, Springer Science and Business Media, Berlin, vol. 80.
14. Gurman, V.I. 2003, “Turnpike solutions in the procedures seeking optimal controls”, Automation and Remote Control, vol. 64, no. 3, pp. 399–408.
15. Tr´elat, E. 2023, “Linear turnpike theorem”, Mathematics of Control, Signals, and Systems, vol. 35, no. 3, pp. 685–739.
Review
For citations:
Gorelik V.A., Zolotova T.V. Two-criteria optimal control problem using Germeier convolution. Chebyshevskii Sbornik. 2026;27(1):51-62. (In Russ.) https://doi.org/10.22405/2226-8383-2018-27-1-51-62
Views:
384
JATS XML
Email this article 