Definition
A firm needs to keep cash, either in the form of cash on hand or as a bank deposit, to meet its daily transaction requirements. Daily inflows and outflows of cash are random. There is a finite target for the cash balance, which could be zero in some cases. The firm wants to select a policy that minimizes the expected total discounted cost for being far away from the target during some time horizon. This time horizon is usually infinity. The firm has an incentive to keep the cash level low, because each unit of positive cash leads to a holding cost since cash has alternative uses like dividends or investments in earning assets. The firm has an incentive to keep the cash level high, because penalty costs are generated as a result of delays in meeting demands for cash. The firm can increase its cash balance by raising new capital or by selling some earnings assets, and it can reduce its cash balance by paying dividends or investing in earning assets. This control of the cash...
Bibliography
Bensoussan A, Lions JL (1973) Nouvelle formulation de problemes de controle impulsionnel et applications. C R Acad Sci (Paris) Ser A 276:1189–1192
Bensoussan A, Lions JL (1975) Nouvelles methodes en controle impulsionnel. Appl Math Opt 1:289–312
Bensoussan A, Lions JL (1982) Controle impulsionnel et inequations quasi variationelles. Bordas, Paris
Cadenillas A, Zapatero F (1999) Optimal Central Bank intervention in the foreign exchange market. J Econ Theory 87:218–242
Cadenillas A, Lakner P, Pinedo M (2010) Optimal control of a mean-reverting inventory. Oper Res 58:1697–1710
Constantinides GM (1976) Stochastic cash management with fixed and proportional transaction costs. Manage Sci 22:1320–1331
Constantinides GM, Richard SF (1978) Existence of optimal simple policies for discounted-cost inventory and cash management in continuous time. Oper Res 26:620–636
Eppen GD, Fama EF (1968) Solutions for cash balance and simple dynamic portfolio problems. J Bus 41:94–112
Eppen GD, Fama EF (1969) Cash balance and simple dynamic portfolio problems with proportional costs. Int Econ Rev 10:119–133
Feng H, Muthuraman K (2010) A computational method for stochastic impulse control problems. Math Oper Res 35:830–850
Girgis NM (1968) Optimal cash balance level. Manage Sci 15:130–140
Harrison JM, Sellke TM, Taylor AJ (1983) Impulse control of Brownian motion. Math Oper Res 8:454–466
Hasbrouck J (2007) Empirical market microstructure. Oxford University Press, New York
Madhavan A, Smidt S (1993) An analysis of changes in specialist inventories and quotations. J Finance 48:1595–1628
Manaster S, Mann SC (1996) Life in the pits: competitive market making and inventory control. Rev Financ Stud 9:953–975
Neave EH (1970) The stochastic cash-balance problem with fixed costs for increases and decreases. Manage Sci 16:472–490
Ormeci M, Dai JG, Vande Vate J (2008) Impulse control of Brownian motion: the constrained average cost case. Oper Res 56:618–629
Vial JP (1972) A continuous time model for the cash balance problem. In: Szego GP, Shell C (eds) Mathematical methods in investment and finance. North Holland, Amsterdam
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Cadenillas, A. (2014). Cash Management. In: Baillieul, J., Samad, T. (eds) Encyclopedia of Systems and Control. Springer, London. https://doi.org/10.1007/978-1-4471-5102-9_45-1
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DOI: https://doi.org/10.1007/978-1-4471-5102-9_45-1
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Cash Management- Published:
- 22 October 2020
DOI: https://doi.org/10.1007/978-1-4471-5102-9_45-2
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Cash Management- Published:
- 08 July 2014
DOI: https://doi.org/10.1007/978-1-4471-5102-9_45-1