A hyperbolic model of optimal cash balances

References

• Abramowitz, M., and I. Stegun. 1964. Handbook of Mathematical Functions with Formulas, Graphs, and Mathematical Tables. Washington, DC: NBS Applied Mathematics Series 55, National Bureau of Standards.
   Google Scholar
• Arnold, L. 1974. Stochastic Differential Equations. New York: Wiley.
   Google Scholar
• Avni, Y. 1976. “Energy Spectra of X-Ray Clusters of Galaxies.” Astrophysical Journal 210: 642–646.
   Google Scholar
• Baccarin, S. 2009. “Optimal Impulse Control for a Multidimensional Cash Management System with Generalized Cost Functions.” European Journal of Operational Research 196 (1): 198–206. doi: 10.1016/j.ejor.2008.02.040
   Web of Science ®Google Scholar
• Bartlett, M. 1955. An Introduction to Stochastic Processes. Cambridge: Cambridge University Press.
   Google Scholar
• Berkson, J. 1980. “Minimum Chi-Square, Not Maximum Likelihood!.” The Annals of Statistics 8 (3): 457–487. doi: 10.1214/aos/1176345003
   Web of Science ®Google Scholar
• Black, F. 1995. “Interest Rates as Options.” The Journal of Finance 50 (5): 1371–1376. doi: 10.1111/j.1540-6261.1995.tb05182.x
   Web of Science ®Google Scholar
• Boyce, W., and R. DiPrima. 2005. Elementary Differential Equations and Boundary Value Problems. New York: Wiley.
   Google Scholar
• Carnahan, B., H. Luther, and J. Wilkes. 1969. Applied Numerical Analysis. New York: Wiley.
   Google Scholar
• Chen, J., D. Ma, X. Song, and M. Tippett. 2017. “Negative Real Interest Rates.” The European Journal of Finance 23 (15): 1447–1467. doi: 10.1080/1351847X.2016.1158729
   Web of Science ®Google Scholar
• Conover, W. 1980. Practical Nonparametric Statistics. New York: Wiley.
   Google Scholar
• Constantinides, G. 1976. “Stochastic Cash Management with Fixed and Proportional Transaction Costs.” Management Science 22 (12): 1320–1331. doi: 10.1287/mnsc.22.12.1320
   Web of Science ®Google Scholar
• Cox, J. C., J. E. Ingersoll, and S. A. Ross. 1985. “A Theory of the Term Structure of Interest Rates.” Econometrica 53 (2): 385–407. doi: 10.2307/1911242
   Web of Science ®Google Scholar
• Cox, D., and H. Miller. 1965. Theory of Stochastic Processes. London: Chapman and Hall.
   Google Scholar
• da Costa Moraes, M., M. Nagano, and V. Sobreiro. 2015. “Stochastic Cash Flow Management Models: A Literature Review Since the 1980s.” In Decision Models in Engineering and Management, edited by P. Guarnieri, 11–28. Cham: Springer.
   Google Scholar
• Cramér, H. 1946. Mathematical Methods of Statistics. Princeton, NJ: Princeton University Press.
   Google Scholar
• Daellenbach, H. 1971. “A Stochastic Cash Balance Model with Two Sources of Short-Term Funds.” International Economic Review 12 (2): 250–256. doi: 10.2307/2525685
   Google Scholar
• Eppen, G. D., and E. D. Fama. 1969. “Cash Balance and Simple Dynamic Portfolio Problems with Proportional Costs.” International Economic Review 10 (2): 119–133. doi: 10.2307/2525547
   Google Scholar
• Frenkel, J., and B. Jovanovic. 1978. On Transactions and Precautionary Demand for Money. National Bureau of Economic Research Working Paper Series, No. 288. doi:10.3386/w0288.
   Google Scholar
• Gormley, F., and N. Meade. 2007. “The Utility of Cash Flow Forecasts in the Management of Corporate Cash Balances.” European Journal of Operational Research 182 (2): 923–935. doi: 10.1016/j.ejor.2006.07.041
   Web of Science ®Google Scholar
• Grigelionis, B. 2013. Student’s t-Distribution and Related Stochastic Processes. Heidelberg: Springer.
   Google Scholar
• Guo, Q., H. Rhys, X. Song, and M. Tippett. 2016. “The Friedman Rule and Inflation Targeting.” The European Journal of Finance 22 (14): 1414–1434. doi: 10.1080/1351847X.2014.953700
   Web of Science ®Google Scholar
• Hall, A. 2005. Generalized Method of Moments. Oxford: Oxford University Press.
   Google Scholar
• Heinrich, J. 2004. A Guide to the Pearson Type IV Distribution. Note 6820, Collider Dectector at Fermilab, Fremilab, Batavia, IL.
   Google Scholar
• Higson, A., S. Yoshikatsu, and M. Tippett. 2010. “Organization Size and the Optimal Investment in Cash.” IMA Journal of Management Mathematics 21 (1): 27–38. doi: 10.1093/imaman/dpp015
   Web of Science ®Google Scholar
• Hinderer, K., and K. Waldmann. 2001. “Cash Management in a Randomly Varying Environment.” European Journal of Operational Research 130 (3): 468–485. doi: 10.1016/S0377-2217(99)00398-7
   Web of Science ®Google Scholar
• Jarque, C., and A. Bera. 1980. “Efficient Tests for Normality, Homoscedasticity and Serial Independence of Regression Residuals.” Economics Letters 6 (3): 255–259. doi: 10.1016/0165-1765(80)90024-5
   Web of Science ®Google Scholar
• Jones, M., and A. Pewsey. 2009. “Sinh-Arcsinh Distributions.” Biometrika 96 (4): 761–780. doi: 10.1093/biomet/asp053
   Web of Science ®Google Scholar
• Karlin, S., and H. Taylor. 1981. A Second Course in Stochastic Processes. London: Academic Press.
   Google Scholar
• Kendall, M., and A. Stuart. 1977. Advanced Theory of Statistics: Volume 1. London: Charles Griffin & Company.
   Google Scholar
• Kendall, M., and A. Stuart. 1979. Advanced Theory of Statistics: Volume 2. London: Charles Griffin & Company.
   Google Scholar
• Keynes, J. 1936. The General Theory of Employment, Interest and Money. London: MacMillan and Company Ltd.
   Google Scholar
• Leonenko, G., and T. Phillips. 2012. “High-order Approximation of Pearson Diffusion Processes.” Journal of Computational and Applied Mathematics 236: 2853–2868. doi: 10.1016/j.cam.2012.01.022
   Web of Science ®Google Scholar
• Mallaris, A. 1989. “Approaches to the Cash Management Problem.” Advances in Financial Planning and Forecasting, 3: 231–243.
   Google Scholar
• Merton, R. 1969. “Lifetime Portfolio Selection Under Uncertainty: The Continuous-Time Case.” The Review of Economics and Statistics 51 (3): 247–257. doi: 10.2307/1926560
   Web of Science ®Google Scholar
• Miller, M., and D. Orr. 1966. “A Model of the Demand for Money by Firms.” The Quarterly Journal of Economics 80 (3): 413–435. doi: 10.2307/1880728
   Web of Science ®Google Scholar
• Møller, J., and H. Madsen. 2010. From State Dependent Diffusion to Constant Diffusion in Stochastic Differential Equations by the Lamperti Transform. Kgs. Lyngby, Denmark: Technical University of Denmark, DTU Informatics, Building 321 (IMM-Technical Report-2010-16).
   Google Scholar
• Mood, A., F. Graybill, and D. Boes. 1974. Introduction to the Theory of Statistics. New York: McGraw-Hill.
   Google Scholar
• Nagahara, Y. 1999. “The PDF and CF of Pearson Type IV Distributions and the ML Estimation of the Parameters.” Statistics & Probability Letters 43 (3): 251–264. doi: 10.1016/S0167-7152(98)00265-X
   Web of Science ®Google Scholar
• Patinkin, D. 1965. Money, Interest and Prices. Evanston, IL: Harper & Row.
   Google Scholar
• Premachandra, I. 2004. “A Diffusion Approximation Model for Managing Cash in Firms: An Alternative Approach to the Miller-Orr Model.” European Journal of Operational Research 157 (1): 218–226. doi: 10.1016/S0377-2217(03)00109-7
   Web of Science ®Google Scholar
• Shaw, W., and M. Schofield. 2015. “A Model of Returns for the Post-Credit-Crunch Reality: Hybrid Brownian Motion with Price Feedback.” Quantitative Finance 15 (6): 975–998. doi: 10.1080/14697688.2011.642810
   Web of Science ®Google Scholar
• Smith, G. 1986. “A Dynamic Baumol-Tobin Model of Money Demand.” The Review of Economic Studies 53 (3): 465–469. doi: 10.2307/2297641
   Web of Science ®Google Scholar
• Tapiero, C., and D. Zuckerman. 1980. “A Note on the Optimal Control of a Cash Balance Problem.” Journal of Banking & Finance 4 (4): 345–352. doi: 10.1016/0378-4266(80)90013-8
   Web of Science ®Google Scholar
• Uhlenbeck, G., and L. Ornstein. 1930. “On the Theory of the Brownian Motion.” Physical Review 36 (5): 823–841. doi: 10.1103/PhysRev.36.823
   Google Scholar
• Vial, J. P. 1970. A Continuous Time Model for the Cash Balance Problem. Center for Operations Research & Econometrics.
   Google Scholar
• Walker, H. 1940. “Degrees of Freedom.” Journal of Educational Psychology 31 (4): 253–269. doi: 10.1037/h0054588
   Google Scholar
• Wang, Z., G. Xu, P. Zhao, and Z. Lu. 2018. “The Optimal Cash Holding Models for Stochastic Cash Management of Continuous Time.” Journal of Industrial and Management Optimization 14 (1): 1–17.
   Web of Science ®Google Scholar
• Yao, J., M. Chen, and H. Lu. 2006. “A Fuzzy Stochastic Single-Period Model for Cash Management.” European Journal of Operational Research 170 (1): 72–90. doi: 10.1016/j.ejor.2004.06.017
   Web of Science ®Google Scholar