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Optimal Cash Management Under Uncertainty

Author

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  • Bensoussan, Alain
  • Chutani, Anshuman
  • Sethi, Suresh

Abstract

We solve an agent's optimization problem of meeting demands for cash over time with cash deposited in bank or invested in stock. The stock pays dividends and uncertain capital gains, and a commission is incurred in buying and selling of stock. We use a stochastic maximum principle to obtain explicitly the optimal transaction policy.

Suggested Citation

  • Bensoussan, Alain & Chutani, Anshuman & Sethi, Suresh, 2009. "Optimal Cash Management Under Uncertainty," MPRA Paper 19896, University Library of Munich, Germany.
    • Handle: RePEc:pra:mprapa:19896
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    References listed on IDEAS

    as
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    8. Gary D. Eppen & Eugene F. Fama, 1971. "Three Asset Cash Balance and Dynamic Portfolio Problems," Management Science, INFORMS, vol. 17(5), pages 311-319, January.
    9. Suresh P. Sethi, 2021. "Optimal Control Theory," Springer Texts in Business and Economics, Springer, edition 4, number 978-3-030-91745-6, August.
    10. 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.
    11. Merton H. Miller & Daniel Orr, 1966. "A Model of the Demand for Money by Firms," The Quarterly Journal of Economics, President and Fellows of Harvard College, vol. 80(3), pages 413-435.
    12. Ioannis Karatzas & John P. Lehoczky & Suresh P. Sethi & Steven E. Shreve, 1986. "Explicit Solution of a General Consumption/Investment Problem," Mathematics of Operations Research, INFORMS, vol. 11(2), pages 261-294, May.
    13. M. H. A. Davis & A. R. Norman, 1990. "Portfolio Selection with Transaction Costs," Mathematics of Operations Research, INFORMS, vol. 15(4), pages 676-713, November.
    14. Vickson, R. G., 1985. "Simple Optimal Policy for Cash Management: The Average Balance Requirement Case," Journal of Financial and Quantitative Analysis, Cambridge University Press, vol. 20(3), pages 353-369, September.
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    Citations

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    Cited by:

    1. Alvarez, Fernando & Lippi, Francesco, 2013. "The demand of liquid assets with uncertain lumpy expenditures," Journal of Monetary Economics, Elsevier, vol. 60(7), pages 753-770.
    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. Schroeder, Pascal & Kacem, Imed, 2020. "Competitive difference analysis of the cash management problem with uncertain demands," European Journal of Operational Research, Elsevier, vol. 283(3), pages 1183-1192.
    4. Guangchen Wang & Hua Xiao, 2015. "Arrow Sufficient Conditions for Optimality of Fully Coupled Forward–Backward Stochastic Differential Equations with Applications to Finance," Journal of Optimization Theory and Applications, Springer, vol. 165(2), pages 639-656, May.
    5. Yonit Barron, 2022. "A probabilistic approach to the stochastic fluid cash management balance problem," Annals of Operations Research, Springer, vol. 312(2), pages 607-645, May.
    6. David Orrell, 2018. "Quantum Economics," Economic Thought, World Economics Association, vol. 7(2), pages 63-81, November.
    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.
    8. García Cabello, Julia, 2017. "The future of branch cash holdings management is here: New Markov chains," European Journal of Operational Research, Elsevier, vol. 259(2), pages 789-799.
    9. Van Son Lai & Duc Khuong Nguyen & William Sodjahin & Issouf Soumaré, 2018. "Discretionary Idiosyncratic Risk, Firm Cash Holdings and Investment," Working Papers 2018-008, Department of Research, Ipag Business School.

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    More about this item

    Keywords

    Cash management; Stochastic control; Maximum principle; Risky assets;
    All these keywords.

    JEL classification:

    • G31 - Financial Economics - - Corporate Finance and Governance - - - Capital Budgeting; Fixed Investment and Inventory Studies
    • E22 - Macroeconomics and Monetary Economics - - Consumption, Saving, Production, Employment, and Investment - - - Investment; Capital; Intangible Capital; Capacity
    • C02 - Mathematical and Quantitative Methods - - General - - - Mathematical Economics
    • C61 - Mathematical and Quantitative Methods - - Mathematical Methods; Programming Models; Mathematical and Simulation Modeling - - - Optimization Techniques; Programming Models; Dynamic Analysis
    • D92 - Microeconomics - - Micro-Based Behavioral Economics - - - Intertemporal Firm Choice, Investment, Capacity, and Financing
    • D14 - Microeconomics - - Household Behavior - - - Household Saving; Personal Finance

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