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

This paper introduces continuous and discrete modern control theory, especially the free-end point versions of the maximum principle, to the field of finance. We shall not, however, go into the proofs and other mathematical details because they are available in the cited literature. Instead, we shall briefly review the continuous and discrete maximum principles and then model simple cash balance problems as problems in control theory. we shall be especially intersted in the financial interpretations of the various functions such as the Hamiltonian function and the adjoint functions that arise in the course of the situation. Thus, we illustrate how such problems can be solved by simply capitalizing on the available control theory literature