A Note on Modeling Simple Dynamic Cash Balance Problems - Sethi, Suresh P. (Journal of Financial and Quantitative Analysis, 1973)
In [2]Sethi and Thompson illustrated the applications of the maximum principle to solve simple dynamic cash balance problems. In Section IV of that paper, we introduced the idea of penalty function to solve the cash balance problem with bounded state variables arising out of disallowing overdrafts and short selling. This resulted in the adjoint equations containing terms in the state variables x(t) and y(t). We then stated the need for solving a two-point boundary value problem.