DOI QR코드

DOI QR Code

Optimal Control for Cash Management with Investment and Retrieval

투자와 회수를 고려한 기업의 최적 현금 관리

  • Kim, Eun-Gab (College of Business Administration, Ewha Womans University) ;
  • Byun, Jin-Ho (College of Business Administration, Ewha Womans University) ;
  • Pae, Jae-Hyun (College of Business Administration, Ewha Womans University)
  • 김은갑 (이화여자대학교 경영대학) ;
  • 변진호 (이화여자대학교 경영대학) ;
  • 배재현 (이화여자대학교 경영대학)
  • Received : 2011.05.14
  • Accepted : 2011.08.05
  • Published : 2011.12.01

Abstract

We develop a cash management model in which firms face randomly occurred investment projects and retrieve investments upon the maturity of these projects. Using the Markov Decision Problem approach, we examine a control policy which dynamically adjusts the cash balance under the discounted cost criterion. The existence of an optimal policy is shown under some conditions. The optimal solution procedure is developed to find the optimal points and the optimal sizes for adjusting the cash balance. In numerical experiment, we investigate important structural properties of the optimal cash management policy.

Keywords

References

  1. Baccarin, S. (2002), Optimal impulse control for cash management with quadratic holding-penalty costs, Decisions in Economics and Finance, 25, 19-32. https://doi.org/10.1007/s102030200001
  2. Baumol, W. (1952), The transactions demand for cash : an inventory theoretic approach, The Quarterly Journal of Economics, 66, 545-556. https://doi.org/10.2307/1882104
  3. Bensoussan, A., Chutani, A., and Sethi, S. (2009), Optimal cash management under uncertainty, Working Paper, School of Management, The University of Texas at Dallas.
  4. Black, R. and Telmer, C. (1999), Liability management using dynamic portfolio strategies, ALGO Research Quarterly, 2(3).
  5. Constantinides, G. and Richard, S. (1978), Existence of optimal simple policies for discounted-cost inventory and cash management in continuous time, Operations Research, 26, 620-636. https://doi.org/10.1287/opre.26.4.620
  6. Dittmar, A. and Mahrt-Smith, J. (2007), Corporate governance and the value of cash holdings, Journal of Financial Economics, 83, 599-634. https://doi.org/10.1016/j.jfineco.2005.12.006
  7. Eppen, G. D. and Fama, E. F. (1969), Cash balance and simple dynamic portfolio problems with proportional costs, International Economic Review, 10, 119-133. https://doi.org/10.2307/2525547
  8. Feinburg, E. and Lewis, M. (2005), Optimality of four-threshold policies in inventory systems with customer returns and borrowing/storage options, Probability in the Engineering and Informational Sciences, 19, 45-71
  9. Girgis, N. M. (1968), Optimal cash balance levels, Management Science, 15, 130-140 https://doi.org/10.1287/mnsc.15.3.130
  10. Harrison, J. M., Sellke, T., and Taylor, A. (1983), Impulse control of brownian motion, Mathematics of Operations Research, 8, 454-466. https://doi.org/10.1287/moor.8.3.454
  11. Hugonniery, J., Malamudz, S., and Morellec, E. (2011), Capital supply uncertainty, cash holdings, and investment, Working paper.
  12. Lippman, S. (1975), Applying a new device in the optimization of Exponential queueing systems, Operations Research, 23, 687-710. https://doi.org/10.1287/opre.23.4.687
  13. Miller, M. and Orr, D. (1966), A model of the demand for money by firms, The Quarterly Journal of Economics, 81, 413-435.
  14. Neave, E. H. (1970), The stochastic cash balance problem with fixed costs for increases and decreases, Management Science, 16, 472-490. https://doi.org/10.1287/mnsc.16.7.472
  15. Ogden, W. and Sundaram, S. (1998), A model for optimal utilization of a firmʼs line of credit, Journal of Financial And Strategic Decisions, 11(1), 27-36.
  16. Porteus, E. (1982), Conditions for Characterizing the Structure of Optimal Strategies in Infinite-Horizon Dynamic Programs, Journal of Optimization Theory and Applications, 36, 419-432. https://doi.org/10.1007/BF00934355
  17. Premachandra, I. M. (2004), A diffusion approximation model for managing cash in firms : An alternative approach to the Miller-Orr model, European Journal of Operational Research, 157, 218-226. https://doi.org/10.1016/S0377-2217(03)00109-7
  18. Puterman, M. (2005), Markov Decision Processes, John Wiley and Sons.
  19. Sato, K. and Sawaki, K. (2009), Optimal impulse control for cash management with two sources of short-term funds, The Eighth International Symposium on Operations Research and Its Applications, 323-331.
  20. Schmid, O. (2011), A multistage stochastic optimization model for the cash management problem, Working Paper.