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Optimal Cash Management Under Uncertainty

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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.

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File URL: http://mpra.ub.uni-muenchen.de/19896/
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Bibliographic Info

Paper provided by University Library of Munich, Germany in its series MPRA Paper with number 19896.

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Date of creation: 25 Feb 2009
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Publication status: Published in Operations Research Letters 6.37(2009): pp. 425-429
Handle: RePEc:pra:mprapa:19896

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

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References

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  1. George M. Constantinides, 1976. "Stochastic Cash Management with Fixed and Proportional Transaction Costs," Management Science, INFORMS, vol. 22(12), pages 1320-1331, August.
  2. Vasicek, Oldrich, 1977. "An equilibrium characterization of the term structure," Journal of Financial Economics, Elsevier, vol. 5(2), pages 177-188, November.
  3. 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.
  4. 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.
  5. 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.
  6. Hull, John & White, Alan, 1990. "Pricing Interest-Rate-Derivative Securities," Review of Financial Studies, Society for Financial Studies, vol. 3(4), pages 573-92.
  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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Cited by:
  1. Fernando Alvarez & Francesco Lippi, 2012. "The Demand of Liquid Assets with Uncertain Lumpy Expenditures," NBER Working Papers 18152, National Bureau of Economic Research, Inc.

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