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A Note on Modeling Simple Dynamic Cash Balance Problems

Published online by Cambridge University Press:  19 October 2009

Suresh P. Sethi
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Extract

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.

Type
Communications
Information
Journal of Financial and Quantitative Analysis , Volume 8 , Issue 4 , September 1973 , pp. 685 - 687
Copyright
Copyright © School of Business Administration, University of Washington 1973

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References

[1]Segers, R. G. “A Generalized Function Setting for Dynamic Optimal Control Problems.” ESSO Mathematics and Research, Inc., July 1971.Google Scholar
[2]Sethi, S. P., and Thompson, G. L.. “Application of Mathematical Control Theory to Finance: Modeling Simple Dynamic Cash Balance Problems.” Journal of Financial and Quantitative Analysis, vol. 5 (December 1970), pp. 381–394.CrossRefGoogle Scholar