Hostname: page-component-78c5997874-dh8gc Total loading time: 0 Render date: 2024-11-12T21:24:50.749Z Has data issue: false hasContentIssue false
  • English
  • Français

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

Published online by Cambridge University Press:  19 October 2009

Suresh P. Sethi  and
Gerald L. Thompson
Get access Rights & Permissions [Opens in a new window]

Extract

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.

Type
Research Article
Information
Journal of Financial and Quantitative Analysis , Volume 5 , Issue 4-5 , December 1970 , pp. 381 - 394
Copyright
Copyright © School of Business Administration, University of Washington 1970

Access options

Get access to the full version of this content by using one of the access options below. (Log in options will check for institutional or personal access. Content may require purchase if you do not have access.)

References

[1]Beals, P., “Pontryagin's Maximum Principle: A Tool for Evaluation and Control of Dynamic Managerial Systems” (Thesis Proposal, University of Massachusetts, Boston, November 1969).Google Scholar
[2]Berkovitz, L. D., “On Control Problems with Bounded State Variables,” Journal of Math Analysis and Application, Vol. 5, No. 3 (1962).Google Scholar
[3]Canon, M.D., Cullum, C. D. Jr., and Polak, E., Theory of Optimal Control and Mathematical Programming (McGraw-Hill, 1970).Google Scholar
[4]Cohen, K. J., “Portfolio Approaches in Finance,” Working Paper No. 61–68–9, GSIA (Pittsburgh, Pa.: Carnegie-Mellon University, 1969).Google Scholar
[5]Ijiri, Y., and Thompson, G. L., “Applications of Mathematical Control Theory to Accounting and Budgeting: I. The Continuous Wheat Trading Model,” Accounting Review, XLV(1970), pp. 246–258.Google Scholar
[6]Ijiri, Y., “Applications of Mathematical Control Theory to Accounting and Budgeting: II. The Continuous Joint Trading Model,” Management Science Research Report No. 163, GSIA (Pittsburgh, Pa.: Carnegie-Mellon University, 1969).Google Scholar
[7]Ijiri, Y., “Applications of Mathematical Control Theory to Accounting and Budgeting: III. The Discrete Wheat Trading and Discrete Joint Production Models,” Management Science Research Report, GSIA (Pittsburgh, Pa.: Carnegie-Mellon University, forthcoming).Google Scholar
[8]Jacobson, D. H., Lele, M. M. and Speyer, J. L., “New Necessary Conditions of Optimality for Control Problems with State Variable Inequality Constraints,” Technical Report #597(Harvard University, Division of Engineering and Applied Physics, August 1969).Google Scholar
[9]Kamlen, M. I. and Schwartz, N. L., “Optimal Maintenance and Sale Age for a Machine Subject to Failure,” W.P. #60–69–7, GSIA (Pittsburgh, Pa.: Carnegie-Mellon University, January 1970).Google Scholar
[10]Kleindorfer, G. B., Kleindorfer, P. R. and Thompson, G. L., “The Discrete Maximum Principle with Applications to Management Science,” Management Science Research Report No. 137, GSIA (Pittsburgh, Pa.: Carnegie-Mellon University, 1968).Google Scholar
[11]Lee, E. B., and Marcus, L., Foundation of Optimal Control Theory (New York: John Wiley & Sons, 1967).Google Scholar
[12]Nelson, R. T., “Labor Assignment As a Special Dynamic Control Problem,” Operations Research, Vol. 15, No. 1 (1967), pp. 139–146.Google Scholar
[13]Pontryagin, L. S., et al. , The Mathematical Theory of Optimal Processes (New York: John Wiley & Sons, 1962).Google Scholar
[14]Sethi, S. P., “A Note on Planning Horizon Model of Cash Management,”Journal of Quantitative and Financial Analysis, March 1971 (forthcoming).CrossRefGoogle Scholar
[15]Sworder, D. D., “Control of a Linear Discrete-Time Stochastic System with a Bounded Input,”Proc. 1966 Joint Aut. Control Conference(1966), pp. 450–456.Google Scholar
[16]Thompson, R. G., and George, M. D., “Optimal Operations and Investments of the Firm,” Management Science, Vol. 15, No. 1 (September 1968), pp. 49–56.CrossRefGoogle Scholar
[17]Thompson, G. L., “Optimal Maintenance and the Sale Date of a Machine,” Management Science, Vol. 14, No. 9 (May 1968), pp. 543–550.CrossRefGoogle Scholar
[18]Thompson, Gerald L., “Mathematical Control Theory with Applications to Management Science,” in Management Science in Planning and Control (Technical Association of the Pulp and Paper Industry, 1969), pp. 303–320.Google Scholar