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.