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Zhurnal Vychislitel'noi Matematiki i Matematicheskoi Fiziki, 2023, Volume 63, Number 10, Pages 1747–1760
DOI: https://doi.org/10.31857/S0044466923100150 (Mi zvmmf11640) 		 
Computer science

Mathematical model of human capital dynamics

N. V. Trusovabc, A. A. Shananinabcde

a Federal Research Center "Computer Science and Control" of Russian Academy of Sciences, 119333, Moscow, Russia
b Moscow Center for Fundamental and Applied Mathematics, 119991, Moscow, Russia
c FSBI "All-Russian Scientific-Research Institute of Labor" of the Ministry of Labor and Social Protection of the Russian Federation, 105043, Moscow, Russia
d Moscow Institute of Physics and Technology (National Research University), Dolgoprudny, Moscow Region
e Peoples' Friendship University of Russia, 117198, Moscow, Russia
DOI: https://doi.org/10.31857/S0044466923100150
Abstract: A mathematical description of household economic behavior is studied. On the one hand, households are consumers that seek to maximize the discounted utility function in an imperfect market of savings and consumer loans. On the other hand, households are workers in the labor market; they receive a wage and seek to enhance their skills to receive a higher wage. An increase in the level of worker’s skill is achieved via investment in human capital. In this paper, a mathematical model of the worker’s behavior in the labor market is represented in the form of an infinite-horizon optimal control problem. A solution existence theorem is proved, and necessary optimality conditions are obtained in the form of Pontryagin’s maximum principle. The model is identified using Russian statistical data for various social layers.
Key words: mathematical modeling, optimal control, infinite-horizon problems, maximum principle, identification problem.
Funding agency Grant number
Russian Science Foundation 23-21-00281
This work was supported by the Russian Science Foundation, project no. 23-21-00281.
Received: 13.03.2023
Revised: 13.03.2023
Accepted: 26.06.2023
English version:
Computational Mathematics and Mathematical Physics, 2023, Volume 63, Issue 10, Pages 1942–1954
DOI: https://doi.org/10.1134/S0965542523100123
Bibliographic databases:
Document Type: Article
UDC: 519.865
Language: Russian
Citation: N. V. Trusov, A. A. Shananin, “Mathematical model of human capital dynamics”, Zh. Vychisl. Mat. Mat. Fiz., 63:10 (2023), 1747–1760; Comput. Math. Math. Phys., 63:10 (2023), 1942–1954
Citation in format AMSBIB
\Bibitem{TruSha23}
\by N.~V.~Trusov, A.~A.~Shananin
\paper Mathematical model of human capital dynamics
\jour Zh. Vychisl. Mat. Mat. Fiz.
\yr 2023
\vol 63
\issue 10
\pages 1747--1760
\mathnet{http://mi.mathnet.ru/zvmmf11640}
\crossref{https://doi.org/10.31857/S0044466923100150}
\elib{https://elibrary.ru/item.asp?id=54648817}
\transl
\jour Comput. Math. Math. Phys.
\yr 2023
\vol 63
\issue 10
\pages 1942--1954
\crossref{https://doi.org/10.1134/S0965542523100123}
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