The Model of the Human Capital Dynamics and Population Behavior in the Labor Market

• Published in: Lobachevskii journal of mathematics Vol. 46; no. 1; pp. 326 - 340
• Main Authors: Shananin, A. A., Trusov, N. V.
• Format: Journal Article
• Language: English
• Published: Moscow Pleiades Publishing 01.01.2025; Springer Nature B.V
• Subjects: Algebra; Analysis; Boundary conditions; Density distribution; Differential equations; Fokker-Planck equation; Geometry; Labor; Mathematical Logic and Foundations; Mathematical models; Mathematics; Mathematics and Statistics; Optimal control; Probability Theory and Stochastic Processes; identification problem; optimal control; 2010 Mathematics Subject Classification: 37A50, 49N45; infinite time horizon; Kolmogorov–Fokker–Planck equation; Lévy process
• ISSN: 1995-0802; 1818-9962
• DOI: 10.1134/S1995080224608452

We describe the mathematical model of a rational representative employee in the labor market. The employee distributes his salary between consumption and investments in his competencies. The salary is described by a stochastic differential equation depending on the employee’s competence. The model is formalized as an optimal control problem with an infinite time horizon. A model of group behavior of employees in the labor market is constructed. The density distribution of the employees by the phase variables is described by the Kolmogorov–Fokker–Planck equation with an integral boundary condition. The model is identified by Russian statistics. The qualitative results of employees’ behavior in the labor market are obtained.