Skip to main content
SpringerLink
Log in

The Asymptotic Behavior of the Optimal Cash Holding Strategy Under a Class of Utility Functions

  • Original Paper
  • Published:
Bulletin of the Iranian Mathematical Society Aims and scope Submit manuscript

Abstract

The present paper makes a research on the optimal cash holding problem in the continuous time under a class of utility functions, and verifies that the limit of the optimal cash holding strategy under a class of utility functions is equal to the optimal cash holding strategy under the power utility function. An empirical analysis is stated at the end of this paper.

This is a preview of subscription content, log in via an institution to check access.

Access this article

Log in via an institution

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Institutional subscriptions

Fig. 1
Fig. 2
Fig. 3
Fig. 4

Similar content being viewed by others

References

  1. Baccarin, S.: Optimal impulse control for cash management with quadratic holding-penalty costs. Decis. Econ. Finance 25, 19–32 (2002)

    Article  MathSciNet  Google Scholar 

  2. Bar-Ilan, A., Perry, D., Stadje, W.: A generalized impulse control model of cash management. Econ. Dyn. Control 28, 1013–1033 (2004)

    Article  MathSciNet  Google Scholar 

  3. Bar-Ilan, A., Lederman, D.: International reserves and monetary policy. Econ. Lett. 97, 170–178 (2007)

    Article  MathSciNet  Google Scholar 

  4. Baumol, W.: The transaction demand for cash an inventory theoretic approach. Quart. J. Econ. 66, 545–646 (1952)

    Article  Google Scholar 

  5. Beckman, S.R., Foreman, J.N.: An experimental test of the Baumol–Tobin transactions demand for money. J. Money Credit Bank. 20(3), 291–305 (1988)

    Article  Google Scholar 

  6. Ben-Bassat, A., Gottlieb, D.: Optimal international reserves and sovereign risks. Int. Econ. 33, 345–362 (1992)

    Article  Google Scholar 

  7. Bensoussan, A., Chutani, A., Sethi, S.P.: Optimal cash management under uncertainty. Oper. Res. Lett. 37, 425–429 (2009)

    Article  MathSciNet  Google Scholar 

  8. Caballero, R.: Consumption puzzles and precautionary savings. J. Monetary Econ. 25, 113–136 (1990)

    Article  Google Scholar 

  9. Chang, F.: Homogeneity and the transactions demand for money. Money Credit Bank 31, 720–730 (1999)

    Article  Google Scholar 

  10. Cong, C., Zhao, P.: Non-cash risk measure on nonconvex sets. Mathematics 6, 186 (2018)

    Article  Google Scholar 

  11. Dixit, A.: A simplied exposition of the theory of optimal control of Brownian motion. Econ. Dyn. Control 15, 657–673 (1991)

    Article  Google Scholar 

  12. Dreze, J., Modigliani, F.: Consumption decisions under uncertainty. J. Econ. Theory 5, 308–335 (1972)

    Article  MathSciNet  Google Scholar 

  13. Eppen, G.D., Fama, E.: Cash balance and simple dynamic portfolio problems with proportional costs. Int. Econ. 10, 119–133 (1969)

    MATH  Google Scholar 

  14. Fleming, W.H., Soner, H.M.: Controlled markov process and viscosity solutions, 1st edn. Spring-Berlin, New York (2006)

    MATH  Google Scholar 

  15. Frenkel, J., Jovanovic, B.: On transactions and precautionary demand for money. Quart. J. Econ. 94, 24–33 (1980)

    Google Scholar 

  16. Frenkel, J., Jovanovic, B.: Optimal international reserves: A stochastic framework. Econ. J. 91, 507–514 (1981)

    Article  Google Scholar 

  17. Girgi, N.: Optimal cash balance levels. Manag. Sci. 15, 130–140 (1968)

    Article  Google Scholar 

  18. Hausman, W.H., Sanchez-Bell, A.: The stochastic cash balance problem with average compensating-balance requirements. Manag. Sci. 21, 849–857 (1975)

    Article  Google Scholar 

  19. Keynes, J.M.: General Theory of Employment, Interest and Currency, Fist Beijing United Publishing Company, Beijing (2013)

    Google Scholar 

  20. Leland, H.: Saving and uncertainty: The precautionary demand for saving. Quart. J. Econ. 82, 465–473 (1968)

    Article  Google Scholar 

  21. Kramkov, D., Schachermayer, W.: The asymptotic elasticity of utility functions and optimal investment in incomplete markets. Ann. Appl. Prob. 9, 904–950 (1999)

    Article  MathSciNet  Google Scholar 

  22. Melo, M.A.S., Bilich, F.: Expectancy balance model for cash flow. J. Econ. Finance 37, 240–252 (2013)

    Article  Google Scholar 

  23. Milbourne, R.: Optimal money holding under uncertainty. Int. Econ. Rev. 24, 685–698 (1983)

    Article  Google Scholar 

  24. Miller, M., Orr, D.: A model of the demand for money by firms. Quart. J. Econ. 80, 413–435 (1966)

    Article  Google Scholar 

  25. Moraes, M.B.C., Nagano, M.S.: Cash management policies by evolutionary models: A comparison using the Miller-Orr model. JISTEM 10, 561–576 (2013)

    Article  Google Scholar 

  26. Myers Stewart, C., Majluf Nicholas, S.: Corporatw financing and investment decisions when firms have information that the investors do not have. J. Financ. Econ. 13, 187–221 (1987)

    Article  Google Scholar 

  27. Opler, T., Pinkowitz, L., Strulz, R.: The determinants and implications of corporate cash holdings. J. Financ. Econ. 52, 3–46 (1999)

    Article  Google Scholar 

  28. Perry, D., Stadje, W.: Risk analysis for a stochastic cash management model with two types of customers. Insur. Math. Econ. 26, 25–36 (2000)

    Article  MathSciNet  Google Scholar 

  29. Rockafellar, R.T.: Convex Analysis, 2nd edn. Princeton University Press, Princeton (1972)

    Google Scholar 

  30. Sethi, S.P., Thompson, G.L.: Application of mathematical control theory to finance. J. Finan. Quant. Anal. 5, 381–394 (1970)

    Article  Google Scholar 

  31. Smith, G.W.: Transactions demand for money with a stochastic, time varying interest rate. Rev. Econ. Stud. 56, 623–633 (1989)

    Article  Google Scholar 

  32. Song, N., Ching, W.K., Siu, T.K., Yiu, K.F.: On optimal cash management under a stochastic volatility model. East Asian J. Appl. Math. 3, 81–92 (2013)

    Article  MathSciNet  Google Scholar 

  33. Tobin, J.: The interest elasticity of the transaction demand for cash. Rev. Econ. Stat. 38, 241–247 (1956)

    Article  Google Scholar 

  34. Vickson, R.G.: Simple optimal policy for cash management: The average balance requirement case. Financ. Quant. al. 20, 353–369 (1985)

    Article  Google Scholar 

  35. Vogel, R.C., Maddala, G.S.: Cross-section estimates of liquid asset demand by manufacturing corporations. J. Fiance 22, 557–575 (1967)

    Article  Google Scholar 

  36. Wang, Z., Xu, G., Zhao, P., Lu, Z.: The optimal cash holding models for stochastic cash management of continuous time. J. Ind. Manag. Optim. 14(1), 1–17 (2018)

    Article  MathSciNet  Google Scholar 

  37. Yong, J., Lou, H.: A Brief Course on Optimal Control Theory. Higher Education Press, Beijing (2006)

    Google Scholar 

  38. Bian, B., Zheng, H.: Turnpike property and convergence rate for an investment model with general utility functions. J. Econ. Dyn. Control 51, 28–49 (2015)

    Article  MathSciNet  Google Scholar 

Download references

Funding

This research was funded by NNSF of China (nos. 11871275 and 11371194).

Author information

Authors and Affiliations

  1. Department of Applied Mathematics, Nanjing University of Science and Technology, Nanjing, 210094, Jiangsu, People’s Republic of China

    Shihan Di, Yingxue Xiang & Peibiao Zhao

Authors
  1. Shihan Di
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Yingxue Xiang
    View author publications

    You can also search for this author in PubMed Google Scholar

  3. Peibiao Zhao
    View author publications

    You can also search for this author in PubMed Google Scholar

Contributions

All authors contribute equally.

Corresponding author

Correspondence to Peibiao Zhao.

Additional information

Communicated by Majid Gazor.

Publisher's Note

Springer Nature remains neutral with regard to jurisdictional claims in published maps and institutional affiliations.

Supported by the NNSF of China (Nos. 11871275; 11371194), Postgraduate Research & Practice Innovation Program of Jiangsu Province.

Rights and permissions

Reprints and permissions

About this article

Check for updates. Verify currency and authenticity via CrossMark

Cite this article

Di, S., Xiang, Y. & Zhao, P. The Asymptotic Behavior of the Optimal Cash Holding Strategy Under a Class of Utility Functions. Bull. Iran. Math. Soc. 48, 849–884 (2022). https://doi.org/10.1007/s41980-021-00550-6

Download citation

  • Received:

  • Revised:

  • Accepted:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s41980-021-00550-6

Keywords

Mathematics Subject Classification

Search

Navigation