Evgeny Kovalenko

Analytical solutions for the Cauchy problem were constructed and numerical methods were proposed in the article. The results apply to the Cauchy problem for a parabolic equation with polynomial dependence on spatial variables and with arbitrary dependence on time variable. On the basis of the proposed analytical solutions and numerical algorithms, methods of construction of various probabilistic parameters were created for the controlled portfolio, which has assets modeled by a system of stochastic differential equations with trends depending on a number of macroeconomic parameters.