Optimal control of the commercial bank investment including the reinvestment processes

Article is devoted to the creation of a mathematical control of the bank investment process. The whole process of building optimal control may be divided into two components: in the first place, there is the identification of the functions describing the liquid capital movement in the bank and, in the second place, the use of these functions in the scheme of dynamic programming. Before this problem was discussed in the article “Optimal control of the bank investment as a factor of economic stability” in the 4th issue for 2012. In the present article considers this modification of the solution, in particular, we use $\mathfrak{R}$($\varphi$) as a function of reinvestment, where $\varphi$ is inflow of liquid capital realized at the previous step of control.