Optimization of Cash Management Fluctuation through Stochastic Processes
- 1 Department of Mathematics, University of Balamand, Al-Koura, Lebanon
- 2 Department of Mathematics, University of Balamand, Al-Koura, Lebanon
- 3 Department of Mathematics, University of Balamand, Al-Koura, Lebanon
- 4 Department of Mathematics, University of Dayton, Dayton, OH, USA
Abstract
In this paper, we study the optimal level of cash for the firm to hold. We model the cash level with inflows and outflows due to deposits and withdrawals; in between, the cash level is a stochastic process where it signals a time to sell. After modeling the continuous jump, we implemented first step analysis method to find the probability of the event with initial cash and we were able to calculate data driven by set of difference equations. These data are used to determine the length of the period of the investment. Then, we adopt the probabilistic decision model where it goes under mathematical optimization. This model let the investor to maximize the probability of success or to stop on one of the largest fortunes using the equation of the principle of optimality. Finally, to solve these optimal equations, we used the result of positive dynamic programming and we elaborated them by proves.
- Baumol, W.J. (1952) The Transactions Demand for Cash: An Inventory Theoretic Approach. The Quarterly Journal of Economics, 66, 545-556. https://doi.org/10.2307/1882104
- Miller, M.H. and Orr, D. (1966) A Model of the Demand for Money by Firms. The Quarterly Journal of Economics, 80, 413-435. https://doi.org/10.2307/1880728
- Tapiero, C.S. and Zuckerman, D. (1980) A Note on the Optimal Control of a Cash Balance Problem. Journal of Banking and Finance, 4, 345-352. https://doi.org/10.1016/0378-4266(80)90013-8
- Hinderer, K. and Waldmann, K.H. (2001) Cash Management in a Randomly Varying Environment. European Journal of Operational Research, 130, 468-485. https://doi.org/10.1016/S0377-2217(99)00398-7
- Guarnieri, P. (Ed.). (2015) Decision Models in Engineering and Management. Springer, Berlin. https://doi.org/10.1007/978-3-319-11949-6
- Yao, J.S., Chen, M.S. and Lu, H.F. (2006) A Fuzzy Stochastic Single-Period Model for Cash Management. European Journal of Operational Research, 170, 72-90. https://doi.org/10.1016/j.ejor.2004.06.017
- Volosov, K., Mitra, G., Spagnolo, F. and Lucas, C. (2005) Treasury Management Model with Foreign Exchange Exposure. Computational Optimization and Applications, 32, 179-207. https://doi.org/10.1007/s10589-005-2059-2
- Gormley, F.M. and Meade, N. (2007) The Utility of Cash Flow Forecasts in the Management of Corporate Cash Balances. European Journal of Operational Research, 182, 923-935. https://doi.org/10.1016/j.ejor.2006.07.041
- Melo, M.A.S. and Bilich, F. (2011) Expectancy Balance Model for Cash Flow. Journal of Economics and Finance, 37, 240-252. https://doi.org/10.1007/s12197-011-9180-0
- Balasubramanian, J. and Grossmann, I.E. (2004) Approximation to Multistage Stochastic Optimization in Multiperiod Batch Plant Scheduling under Demand Uncertainty. Industrial and Engineering Chemistry Research, 43, 3695-3713. https://doi.org/10.1021/ie030308+
- Wu, D. and Ierapetritou, M. (2007) Hierarchical Approach for Production Planning and Scheduling under Uncertainty. Chemical Engineering and Processing, 46, 1129-1140. https://doi.org/10.1016/j.cep.2007.02.021
- The Gambler’s Ruin Problem. (n.d.). http://www.columbia.edu/
- Pinsky, M. and Karlin, S. (2010) An Introduction to Stochastic Modeling. Academic Press.
- Allen, L.J. (2010) An Introduction to Stochastic Processes with Applications to Biology. CRC Press.