On one inverse problem for the Kolmogorov–Fokker–Planck equation

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.