Numerical-analytical solution of the discrete-time tuning problem for an intervention model in the foreign exchange market

The work examines the problem of optimizing external influences (controls) on the process of changing the price of the so-called bi-currency basket on the foreign exchange market of the Russian Federation. The theoretical basis of the approach used is the solution of a stochastic tuning problem with discrete time. Based on the previous statistical analysis, it was established that the stochastic process characterizing the evolution of the bi-currency basket price, under certain conditions, can be quite adequately described by a classical homogeneous Markov chain. In this case, statistical estimates of the transition probabilities of the specified chain were obtained. Necessary auxiliary probabilistic characteristics of the Markov model are numerically determined. For various given cost characteristics, a study of the stationary cost indicator of management efficiency-average specific profit was conducted. Specific numerical solutions to the corresponding optimal control problem are obtained which can be interpreted as optimal external influences (interventions) on the stochastic process under study.