Skip to main content
SpringerLink
Log in

A Survey and Analysis of the Application of the Laplace Transform to Present Value Problems

  • Conference paper
Modelling for Financial Decisions

Part of the book series: Studies in Financial Modelling ((FINANC.MODELL.))

Abstract

This article provides an overview of the current position with regard to the application of the Laplace transform to Present Value problems. The limitations of the use of the Laplace transform are discussed and some ideas for future possible research are presented.

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

Access this chapter

Log in via an institution
Chapter
USD 29.95
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
eBook
USD 84.99
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
Softcover Book
USD 109.99
Price excludes VAT (USA)
  • Compact, lightweight edition
  • Dispatched in 3 to 5 business days
  • Free shipping worldwide - see info

Tax calculation will be finalised at checkout

Purchases are for personal use only

Institutional subscriptions

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  1. Grubbström, R.W., 1967. On the application of the Laplace transform to certain economic problems. Management Science, 13(7): 558–567

    Article  Google Scholar 

  2. Grubbström, R.W.,1966. Värdering av information i feedbackslingan vid en lagerstyrd produktionsprocess, Dept of Industrial Economics and Management, Royal Institute of Technology, Stockholm.

    Google Scholar 

  3. Buck, J.R., and Hill, T.W., 1971. Laplace transforms for the economic analysis of deterministic problems in engineering. The Engineering Economist, 16(4): 247–263.

    Article  Google Scholar 

  4. Buck, J.R., and Hill, T.W., 1975. Additions to the Laplace transform methodology for economic analysis. The Engineering Economist, 20(3): 197–208.

    Article  Google Scholar 

  5. Reisman, A. and Rao, A.K., 1973. Discounted cash flow analysis: stochastic extensions. Publication # 1, Engineering, Economy Division, AIIE, Atlanta, Georgia.

    Google Scholar 

  6. Rosenthal, R.E., 1978. The variance of present worth of cash flows under uncertain timing. The Engineering Economist, 23(3): 163–170.

    Article  Google Scholar 

  7. Zinn, C.D., W.G. Lesso and B. Motazed, 1977. A probabilistic approach to risk analysis in capital investment projects. The Engineering Economist, 22(4): 239–260.

    Article  Google Scholar 

  8. Tanchoco, Jose M.A., J.R. Buck and L.C. Leung, 1981. Modeling and discounting of continuous cash flows under risk. Engineering Costs and Production Economics, 5(3): 205–216.

    Article  Google Scholar 

  9. Perrakis, S., and Henin, C., 1974. The evaluation of risky investments with random timing of cash returns. Management Science, 21(1): 79–86.

    Article  Google Scholar 

  10. Perrakis S., and Sahin, I., 1976. On risky investments with random timing of cash returns and fixed planning horizon. Management Science, 22(7): 799–809.

    Article  Google Scholar 

  11. Barnes, J.W. and Zinn, C.D. and Eldred, B.S., 1978. A methodology for obtaining the probability density function of the present worth of probabilistic cash flow profiles. AIIE Transactions, 10(3): 226–236.

    Article  Google Scholar 

  12. Young, D. and Contreras, L.E., 1975. Expected present worths of cash flows under uncertain timing. The Engineering Economist, 20(4): 257–268.

    Article  Google Scholar 

  13. Joiner, B.L. and Rosenblatt, J.R., 1971. Some properties of the range in samples from Tukey’s symmetric Lambda distributions. JASA, 66: 394–399.

    Google Scholar 

  14. Feller, W., 1966. An introduction to probability theory and its applications. Vol II, John Wiley & Sons, Inc., New York.

    Google Scholar 

  15. Bellman, R.E. and Roth, R.S., 1984. The Laplace transform. World Scientific Publishing Co Pte Ltd.

    Google Scholar 

  16. Fleischer, G.A., 1981. Assessing the relative efficacy of the transform method for discounting periodic cash flows. 1981 ASEE annual conference proceedings, 71-74.

    Google Scholar 

  17. Gurnani, C., 1982. Present worth analysis of deterministic periodic cash flows. The Engineering Economist, 27(2): 101–126.

    Article  Google Scholar 

  18. Beenhakker, H.L., 1975. Sensitivity analysis of the present value of a project. The Engineering Economist, 20(2): 123–149.

    Article  Google Scholar 

  19. Grubbström, R.W., 1979. Mean and variance of the net present value of a payment stream after correction for a stationary stochastic inflation rate. Working paper WP-71, Department of Production Economics. Linköping Institute of Technology, Sweden.

    Google Scholar 

  20. Almond, B. and Remer, D.S., 1979. Models for present-worth analysis of selected industrial cash flow patterns. Engineering and Process Economics, 4: 455–466.

    Article  Google Scholar 

  21. Spiegel, M.R., 1965. Schaum’s outiine of theory and problems of Laplace transforms. McGraw-Hill Inc., New York.

    Google Scholar 

  22. Miller, M.K. and Guy, W.T., 1966. Numerical inversion of the Laplace transform by use of Jacobi polynomials. SIAM Journal on Numerical Analysis, 3(4): 624–635.

    Article  Google Scholar 

  23. Crump, K.S., 1976. Numerical inversion of Laplace transforms using a Fourier series approximation. Journal of the Association for Computing Machinery, 23(1): 89–96.

    Article  Google Scholar 

  24. Hosono, T., 1981. Numerical inversion of Laplace transform and some applications to wave optics. Radio Science, 16(6): 1015–1019.

    Article  Google Scholar 

  25. Buser, S.A., 1986. Laplace transforms as present value rules: A note. The Journal of Finance, Vol. XLI, No. 1: 243–247.

    Article  Google Scholar 

  26. Pistoia, A., 1960. Qualche considerazione su uno schema di operazione finanziaria che prevede il reinvestimento degli interessi, Istituto di Matematica Finanziaria dell’ Università di Torino, 84.

    Google Scholar 

  27. Levi, E., 1961. Problemi di ritardo in matematica finanziaria, Giornale Istituto Italiano Attuari: 194-202.

    Google Scholar 

  28. Malaska, P. and Kinnunen, T., 1986. A model of management goal setting and its dissipative structure. European Journal of Operational Research, 25: 75–84.

    Article  Google Scholar 

  29. Churchill, R.V., 1958. Operational Mathematics, McGraw-Hill Inc., New York.

    Google Scholar 

  30. López Léautaud, José L., 1972. Comment on: “Laplace transforms for the economic analysis of deterministic problems in engineering” by J.R. Buck and T.W. Hill. The Engineering Economist, 17(2): 137–138.

    Article  Google Scholar 

  31. Mullineux, N., and Reed, J.R. and Richardson, R.G., 1973. Multi-dimensional Laplace transforms and non-linear problems. Int. J. Elect Enging. Educ., 11: 5–17.

    Google Scholar 

  32. Dasarathy, B.V., 1971. D-transforms and non-linear systems analysis. Journal of Sound and Vibration, 15(2): 269–273.

    Article  Google Scholar 

  33. Koh, E.L, 1975. Association of variables inn-dimensional Laplace transform, Int. J. Systcms Sci. 6(2): 127–131.

    Article  Google Scholar 

  34. Flower, J.O., 1976. A note on the application of operational methods to certain non-linear problems. Int J. Elect Enging. Educ., 13: 219–223.

    Google Scholar 

  35. Lubbock, J.K. and Bansal, V.S., 1969. Multidimensional Laplace transforms for solution of nonlinear equations. Proc. IEE, 116(12): 2075–2082.

    Google Scholar 

  36. Joshi, S.G. and Srinivasan, P., 1978. Application of Laplace transform technique to the solution of certain third-order non-linear systems. Journal of Sound and Vibration, 57(1): 41–50.

    Article  Google Scholar 

  37. Bussgang, JJ. and Ehrman, L. and Graham J.W., 1974. Analysis of nonlinear systems with multiple inputs. Proceedings of the Institute of Electrical and Electronics Engineers, 62:1088–1119.

    Google Scholar 

  38. Karmakar, S.B., 1980. Approximate analysis of non-linear systems by Laplace transform. Journal of Sound and Vibration, 69(4): 597–602.

    Article  Google Scholar 

  39. Sato, H. and Asada, K., 1988. Laplace transform transient analysis of a non-linear system. Journal of Sound and Vibration, 121(3): 473–479.

    Article  Google Scholar 

  40. Srinivasan, S.K. and Gopalan, M.N., 1973. Probabilistic analysis of a two-unit system with a warm standby and a single repair facility. Operations Research, 21(3): 748–754.

    Article  Google Scholar 

  41. Smith, D.R., 1978. Optimal repair of a series system. Operations Research, 26(4): 653–662.

    Article  Google Scholar 

  42. Takaragi, K. et al., 1985. A probability bound estimation method in Markov reliability analysis. IEEE Transactions on Reliability, R-34(3): 257–261.

    Article  Google Scholar 

  43. Wells, C.E., 1985. An adaptive estimation procedure using the Laplace transformation. IIE Transactions, 17(3): 242–251.

    Article  Google Scholar 

  44. Shanthikumar, J.G., 1986. First failure time of dependent parallel systems with safety periods. Microelectronics and Reliability, 26(5): 955–972.

    Article  Google Scholar 

  45. Gopalan, M.N. and Nagarwalla, H.E., 1986. Cost-benefit analysis of a 1 out of n: G system with variable repair and preventive maintenance rates. International Journal of Quality & Reliability Management, 3(3): 26–32.

    Article  Google Scholar 

  46. Brockkett, P.L. and Golden, L.L., 1987. A class of utility functions containing all the common utility functions. Management Science, 33(8): 955–964.

    Article  Google Scholar 

  47. Vallée, R. and Nicolau E., 1983. Econometric models and generalized Laplace transforms. Econ. Comput Econ. Cybern. Stud. Res., 18(4): 79–82.

    Google Scholar 

  48. Grubbström, R.W. and Lundquist, J., 1975. Theory of Relatively closed systems and applications. Production-Economic Research in Linköping, Profil 2, Linköping.

    Google Scholar 

  49. Grubbström, R.W., 1980. A principle for determining the correct capital costs of work-in-progress and inventory. Int. J. Prod. Res., 18(2): 259–271.

    Article  Google Scholar 

  50. Gurnani, C., 1983. Economic analysis of inventory systems. Int. J. Prod. Res., 21(2): 261–277.

    Article  Google Scholar 

  51. Grubbström, R.W., 1986. “On the dynamics of a simple multi-stage production-inventory system with production rates depending on inventory levels”. In Chikán, A., (Ed.), Inventory in theory and practice, Elsevier, Amsterdam: 539–561.

    Google Scholar 

  52. Asbjørnsen, O.A., 1983. Project evaluation and cash flow forecasting by stochastic simulation. Modeling, Identification and Control, 4(4): 237–254.

    Article  Google Scholar 

  53. Williams, J., 1973. Laplace transforms. George Allen & Unwin Ltd.

    Google Scholar 

  54. Remer, D.S. et al., 1984. The state of the art of present worth analysis of cash flow distributions. Engineering Costs and Production Economics, 7: 257–278.

    Article  Google Scholar 

  55. Grubbström, R.W., 1982. On the choice of investments under the condition of different borrowing and lending rates. Research Report RR-82, Department of Production Economics, Linköping Institute of Technology.

    Google Scholar 

  56. Grubbström, R.W., 1981. On the traditional investment problem. Working Paper WP-95, Department of Production Economics, Linköping Institute of Technology.

    Google Scholar 

  57. Grubbström, R.W., 1976. On the balancing of queueing costs and capacity costs along the assembly line. Proceedings, the Fifth International Seminar on Algorithms for Production Control and Scheduling, Karlovy Vary.

    Google Scholar 

  58. Grubbström, R.W., and Lundquist, J., 1977. The Axsäter integrated production-inventory model interpreted in terms of the theory of relatively closed systems, Journal of Cybernetics, 7: 49–67.

    Article  Google Scholar 

  59. Grubbström, R.W. and Thorstenson, A., 1986. Evaluation of capital costs in a multi-level inventory system by means of the annuity stream principle. European Journal of Operational Research, 24(1): 136–145.

    Article  Google Scholar 

  60. Thorstenson, A., 1988. Capital costs in inventory models-A discounted cash flow approach. Production-Economic Research in Linköping, Profil 8, Linköping.

    Google Scholar 

  61. Cheng, T.C.E., 1985. Analysis of job flow-time in a job-shop. J. Opl. Res. Soc., 36(3): 225–230.

    Google Scholar 

  62. Sivazlian, B.D., 1979. Approximate optimal solution for a D-policy in an M/G/l queuing system. AIIE Transactions, 11(4): 341–343.

    Article  Google Scholar 

  63. Kotiah, T.C.T., 1978. Approximate transient analysis of some queuing systems. Operations Research, 26(2): 333–346.

    Article  Google Scholar 

  64. Harrison, J.M., 1975. A priority queue with discounted linear costs. Operations Research, 23(2): 260–269.

    Article  Google Scholar 

  65. Weber, E., 1956. Complex convolution method applied to non-linear problems. Proceedings of the Symposium on Non-linear Circuit Analysis, Polytechnic Institute of Brooklyn, New York, Vol. 6: 409–427.

    Google Scholar 

  66. Doyon, L.R., 1981. Stochastic modeling of facility security-systems for analytical solutions. Computers & Industrial Engineering, 5(2): 127–138.

    Article  Google Scholar 

  67. Gibley, R.A. and Sundstrom, R., 1975. Some important applications of Laplace transforms. Proceedings of the American Institute for Decision Sciences, P. 93.

    Google Scholar 

  68. Grubbström, R.W. and Jiang, Y., 1989, The z-transform-An approach to present value analysis, Working Paper WP-158, Dept. of Production Economics, Linköping Institute of Technology, Linköping.

    Google Scholar 

  69. Terborgh, G., 1949. Dynamic equipment policy, New York.

    Google Scholar 

Download references

Author information

Authors and Affiliations

  1. Department of Production Economics, Linköping Institute of Technology, S-58183, Linköping, Sweden

    Robert W. Grubbström

  2. Department of Management, Beijing Institute of Light Industry, 100037, Beijing, P.R. of China

    Jiang Yinzhong

Authors
  1. Robert W. Grubbström
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Jiang Yinzhong
    View author publications

    You can also search for this author in PubMed Google Scholar

Editor information

Editors and Affiliations

  1. Erasmus University, P.O. Box 1738, NL-3000 DR, Rotterdam, The Netherlands

    Jaap Spronk

  2. Università di Catania, Corso Italia 55, I-Catania, Italia

    Benedetto Matarazzo

Rights and permissions

Reprints and permissions

Copyright information

© 1991 Springer-Verlag Berlin · Heidelberg

About this paper

Cite this paper

Grubbström, R.W., Yinzhong, J. (1991). A Survey and Analysis of the Application of the Laplace Transform to Present Value Problems. In: Spronk, J., Matarazzo, B. (eds) Modelling for Financial Decisions. Studies in Financial Modelling. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-76761-6_4

Download citation

  • DOI: https://doi.org/10.1007/978-3-642-76761-6_4

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-642-76763-0

  • Online ISBN: 978-3-642-76761-6

  • eBook Packages: Springer Book Archive

Publish with us

Policies and ethics

Search

Navigation