SOLVING THE PROBLEM OF SAVINGS EXPENDITURE OPTIMIZATION

The paper studies the optimal control problem associated with the search for a consumption strategy, subject to the full savings expenditure during the schedule date in order to obtain the maximum total consumption utility, taking into account inflation. The solution the problem of savings optimization is carried out in the framework of the maximum principle for the power function of consumption utility. The considered problem allows an analytical solution depending on the relations between the model parameters. As a result, optimal consumption programs (expenditure of funds) were obtained in terms of maximizing utility functionality.