Algorithmic solution of the problem of optimal control in a dynamic one-sector economic model with discrete time based on the dynamic programming method

The paper studies a new formulation of the optimal control problem in a dynamic one-sector economic model with discrete time. In the task, the states are the values of the specific capital. The control parameter is the proportion of the specific product produced, directed for investment. The study is based on the dynamic programming method. The Bellman equations for the problem are obtained. The optimality of controls satisfying the Bellman equations is proved. An algorithm was created and described in detail that allows one to solve the Bellman functional equations numerically and to find the optimal control strategy for the problem posed.