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A Note on Modeling Simple Dynamic Cash Balance Problem: Errata

Published online by Cambridge University Press:  06 April 2009

Suresh P. Sethi
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Extract

In [2], I gave a solution of an extended cash balance problem which disallows overdrafts and shortselling. This solution is incorrect. To show this, we produce a counterexample constructed by Carl Norstrøm. In the notation of the note [2], let x0 = 0, y0 = 3, d(t) = 0, α = 0, T = 10, M1 = M2 = ∞

and r2 (t) = .1. Applying the procedure in [2] to this problem, we obtain the policy of impulse-selling all the securities at t = 0. On the other hand, it is obvious by inspection that the optimal policy is to keep the securities until t = 5, at which time, turn them into cash by an impulse-sale. We note, in passing, that the solution by inspection in this case is possible because there is no bounds on the control variable.

Type
Research Article
Information
Journal of Financial and Quantitative Analysis , Volume 13 , Issue 3 , September 1978 , pp. 585 - 586
Copyright
Copyright © School of Business Administration, University of Washington 1978

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References

REFERENCES

[1]Segers, R. G. “A Generalized Function Setting for Dynamic Optimal Control Problems.” In Optimization Methods for Resource Allocation, edited by Cottle, R. and Krarup, J.. New York: Crane, Russak & Co., Inc. (1974).Google Scholar
[2]Sethi, S. P. “Note on Modeling Simple Dynamic Cash Balance Problems.” Journal of Financial and Quantitative Analysis (09 1973), pp. 685–687.CrossRefGoogle Scholar
[3]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 (12 1970), pp. 381–394.CrossRefGoogle Scholar
[4]Sethi, S. P., and Thompson, G. L.. Applied Optimal Control and Management Science Applications (forthcoming).Google Scholar