Applications of Mathematical Control Theory to Finance: Modeling Simple Dynamic Cash Balance Problems

Abstract

In this paper we have dealt with several time dependent cash balance models and have solved them using some form of a control theory maximum principle. The kinds of solutions we obtained were intuitively satisfying from a financial analysis point of view. The main effort for the future will be to extend these very simple models to much more realistic and complicated ones. But to do this will require considerable theoretical research in the area of both deterministic and stochastic control theory. We hope that we have demonstrated the usefulness of these theories in the area of finance and we expect many similar applications to be made in the future.