Search

A mathematical description of the household economic behavior with the help of the Kolmogorov–Fokker–Planck equation is studied. This equation describes the dynamics of the household distribution density with respect to two characteristics: financial state and income. The agreement between statistical data and the solution of the Kolmogorov–Fokker–Planck equation is examined using statistical Rosstat data on the economic state of households in Russia. The problem is formalized as minimizing the deviation of the solution to the Kolmogorov–Fokker–Planck equation from the statistical data by managing household consumption. The extremal problem is solved numerically, and numerical results are presented. [ABSTRACT FROM AUTHOR]

The article develops and investigates a new model for the formation of interest rates on consumer loans based on an analysis of commercial interests and the logic of behavior of commercial banks. The model assumes that the borrowers' incomes are described by a geometric Brownian motion. Commercial banks assess the default risk of borrowers. According to the Feynman–Kac formula, the assessment is reduced to solving a boundary value problem for partial differential equations. An analytical solution to this problem is constructed. The model is used to analyze the problem of maintaining consumer credit under the current conditions as a mechanism for social adaptation of households. [ABSTRACT FROM AUTHOR]

An optimal control problem modeling the economic behavior of a representative household is studied. The existence of its solution is proved, necessary optimality conditions in the form of the Pontryagin–Clarke maximum principle are obtained, and an optimal control synthesis is constructed. The model is identified against Russian statistical data. The model is used to analyze consumer crediting in Russia and its influence on the household economy under COVID-19 pandemic conditions. [ABSTRACT FROM AUTHOR]