Efficient algorithms for solving bank activity optimization problems

We consider the two models: the activity of a monopolist bank and the activity of a new bank starting up on the banking services market. Each model involves a multiextremal nonlinear mathematical programming problem. Algorithms for solving these problems rest on those for solving linear programming problems of a special form, for which we give solutions explicitly and count the number of required operations. We prove the existence of a solution for the problem of the activity of a new bank.