On the concept of a stochastic model with control at the moments of the process at the border of a presented subset of multiple states

The work is devoted to the creation and analysis of the general concept of a special stochastic model with controls. The main feature of the model is that the control actions are carried out at times when a stochastic process describing the system under research reaches the boundary of a given subset of the set of states. The control action itself consists in transferring the process from the boundary to one of the internal states of a given subset. In this case, the internal states are interpreted as acceptable and the boundary ones as unacceptable. Control actions are described by a set of discrete probability distributions depending on the boundary state number. Such a set defines a control strategy. The problem of optimal control is formalized as the problem of finding a control strategy that delivers a global extremum to a certain stationary cost-effectiveness indicator, which in terms of its economic content represents the average specific profit arising from a long evolution of the system. The posed problem of optimal control is proposed to be alled the tuning problem. The paper notes that this stochastic model and the corresponding setup problem can be used to study many real phenomena occurring in economic and technical systems. As an example of such a real phenomenon, interventions in the foreign exchange market of the Russian Federation are considered.