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The Stochastic Cash Balance Problem with Average Compensating-Balance Requirements

Author

Listed:
  • Warren H. Hausman

    (University of Rochester)

  • Antonio Sanchez-Bell

    (Business School of the Instituto Tecnologico de Monterrey)

Abstract

We consider the problem of managing two assets, cash and an earning asset, when net cash flows are stochastic and when there are transfer costs for transferring assets from one form to the other. Previous work on the stochastic cash-balance problem has assumed holding costs for holding excess cash and penalty costs for holding insufficient cash, with these costs assessed per period (the same period in which there is a single decision or transfer opportunity and a single random cash flow). This formulation is appropriate when a firm faces minimum (or zero) compensating-balance requirements, but not when the compensating-balance requirement involves an average deposit balance over a number of decision periods. A dynamic programming model is presented which appropriately represents the relevant cost function for a firm facing an average compensating-balance requirement. The dynamic programming solution to a numerical example is compared to that of a static two-sided (s, S) policy; the optimal dynamic programming solution represents an 18% reduction in relevant costs in the example.

Suggested Citation

  • Warren H. Hausman & Antonio Sanchez-Bell, 1975. "The Stochastic Cash Balance Problem with Average Compensating-Balance Requirements," Management Science, INFORMS, vol. 21(8), pages 849-857, April.
    • Handle: RePEc:inm:ormnsc:v:21:y:1975:i:8:p:849-857
    DOI: 10.1287/mnsc.21.8.849
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    Cited by:

    1. Eduardo Jallath-Coria & Tridas Mukhopadhyay & Amir Yaron, 2002. "How Well Do Banks Manage Their Reserves?," NBER Working Papers 9388, National Bureau of Economic Research, Inc.
    2. Ben A. Chaouch, 2018. "Analysis of the stochastic cash balance problem using a level crossing technique," Annals of Operations Research, Springer, vol. 271(2), pages 429-444, December.
    3. Marcos Melo & Feruccio Bilich, 2013. "Expectancy balance model for cash flow," Journal of Economics and Finance, Springer;Academy of Economics and Finance, vol. 37(2), pages 240-252, April.

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