ИСТИНА

The analysis of a representative household models of the Ramsey type is based on the study of the optimal control problem and the construction of a control synthesis. The problem of the optimal control has been investigated, which simulates the economic behavior of a representative household. A theorem on the existence of a solution has been proved, necessary optimality conditions have been obtained in the form of the Pontryagin-Clarke maximum principle, and an optimal control synthesis has been constructed. In condition when the major economic changes in the behavior of a representative household are taking place, it is necessary to study the households in this group in detail. The models describing the evolution of the distribution of households by income and financial positions are relevant for the analysis of strategies for managing the arrears in consumer loans. Based on the concept of mean field games, a model has been constructed and formalized in the form of a system of Hamilton-Jacobi-Bellman and Kolmogorov-Fokker-Planck equations. The model was identified according to Russian statistics. With its help, the problems of the unsecured consumer loan market in Russia were analyzed, the impact on the economic situation of households of the COVID-19 pandemic, which exacerbated the problem of sustainability of the consumer loan market, and measures affecting the economic situation of low-income households.