Creation of a stochastic dynamic one-sector economic model with discrete time and analysis of the corresponding optimal control problem

The work is devoted to the creation of a stochastic dynamic model of optimal control with discrete time within the framework of a one-sector economic system. The basis is a classical deterministic dynamic model of the economic system in which one universal product is produced. This product is divided into investment and consumer components. System management consists in determining the relationship between these components. In this work, it is assumed that the main parameters of the system depend on some random factor that characterizes the influence of the external environment. This factor is described by a homogeneous Markov chain with a finite set of states and a given transition probability matrix. In this work, a stochastic model of the evolution of the system under consideration is constructed which is a two-dimensional Markov process with discrete time. In terms of its economic content, the first component of this process is specific capital and the second is the state of an external random factor. The control parameter or decision at each moment of time represents the share of the specific product produced directed to investment. The recurrent setting of the cost additive indicator of management efficiency is described. The theoretical basis for solving the problem of optimal control is the method of dynamic programming. In this work, a system of Bellman functional equations is obtained, the solution of which is the optimal control strategy.