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

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  • Sethi, Suresh P.
  • Thompson, Gerald L.

Abstract

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.

Suggested Citation

  • Sethi, Suresh P. & Thompson, Gerald L., 1970. "Applications of Mathematical Control Theory to Finance: Modeling Simple Dynamic Cash Balance Problems," Journal of Financial and Quantitative Analysis, Cambridge University Press, vol. 5(4-5), pages 381-394, December.
    • Handle: RePEc:cup:jfinqa:v:5:y:1970:i:4-5:p:381-394_02
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    Cited by:

    1. Karim, Md Aktar Ul & Aithal, Vikram & Bhowmick, Amiya Ranjan, 2023. "Random variation in model parameters: A comprehensive review of stochastic logistic growth equation," Ecological Modelling, Elsevier, vol. 484(C).
    2. Francisco Salas-Molina & Juan A. Rodríguez-Aguilar & Montserrat Guillen, 2023. "A multidimensional review of the cash management problem," Financial Innovation, Springer;Southwestern University of Finance and Economics, vol. 9(1), pages 1-35, December.
    3. David van Wijk, 2023. "Stochastic Control Barrier Functions for Economics," Papers 2312.12612, arXiv.org, revised Feb 2024.
    4. Robert Holman, 2004. "Ekonomická analýza práva [Economic analysis of law]," Politická ekonomie, Prague University of Economics and Business, vol. 2004(4), pages 519-531.
    5. Bensoussan, Alain & Chutani, Anshuman & Sethi, Suresh, 2009. "Optimal Cash Management Under Uncertainty," MPRA Paper 19896, University Library of Munich, Germany.
    6. Michal Slavík, 2004. "Soudobá makroekonomie a teorie optimálního řízení [Contemporary macroeconomics and optimal control theory]," Politická ekonomie, Prague University of Economics and Business, vol. 2004(4), pages 551-561.
    7. Juliana Nascimento & Warren Powell, 2010. "Dynamic Programming Models and Algorithms for the Mutual Fund Cash Balance Problem," Management Science, INFORMS, vol. 56(5), pages 801-815, May.

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