Mathematical modeling of the consumer loan market in Russia under sanctions

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.