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Optimal Cash Management Under Uncertainty

Author

Listed:
  • 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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    File URL: https://mpra.ub.uni-muenchen.de/19896/1/MPRA_paper_19896.pdf
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    References listed on IDEAS

    as
    1. Merton, Robert C., 1971. "Optimum consumption and portfolio rules in a continuous-time model," Journal of Economic Theory, Elsevier, vol. 3(4), pages 373-413, December.
    2. 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(03), pages 353-369, September.
    3. Vasicek, Oldrich, 1977. "An equilibrium characterization of the term structure," Journal of Financial Economics, Elsevier, vol. 5(2), pages 177-188, November.
    4. George M. Constantinides, 1976. "Stochastic Cash Management with Fixed and Proportional Transaction Costs," Management Science, INFORMS, vol. 22(12), pages 1320-1331, August.
    5. Hull, John & White, Alan, 1990. "Pricing Interest-Rate-Derivative Securities," Review of Financial Studies, Society for Financial Studies, vol. 3(4), pages 573-592.
    6. 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.
    7. 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.
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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. 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.
    3. GarcĂ­a 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.

    More about this item

    Keywords

    Cash management; Stochastic control; Maximum principle; Risky assets;

    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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