A survey and analysis of the application of the Laplace transform to present value problems

  • Robert W. Grubbström
  • Jiang Yinzhong


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.


Economic Theory Public Finance Current Position 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.


Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.


  1. [1]
    Grubbström, R.W., 1967. On the application of the Laplace transform to certain economic problems.Management Science,13 (7): 558–567Google Scholar
  2. [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. [3]
    Buck, J.R., andHill, T.W., 1971. Laplace transforms for the economic analysis of deterministic problems in engineering.The Engineering Economist,16 (4): 247–263.Google Scholar
  4. [4]
    Buck, J.R., andHill, T.W., 1975. Additions to the Laplace transform methodology for economic analysis.The Engineering Economist,20 (3): 197–208.Google Scholar
  5. [5]
    Reisman, A. andRao, A.K., 1973.Discounted cash flow analysis: stochastic extensions. Publication #1, Engineering, Economy Division, AIIE, Atlanta, Georgia.Google Scholar
  6. [6]
    Rosenthal, R.E., 1978. The variance of present worth of cash flows under uncertain timing.The Engineering Economist,23 (3): 163–170.Google Scholar
  7. [7]
    Zinn, C.D., W.G. Lesso andB. Motazed, 1977. A probabilistic approach to risk analysis in capital investment projects.The Engineering Economist,22 (4): 239–260.Google Scholar
  8. [8]
    Tanchoco, Jose M.A., J.R. Buck andL.C. Leung, 1981. Modeling and discounting of continuous cash flows under risk.Engineering Costs and Production Economics,5 (3): 205–216.Google Scholar
  9. [9]
    Perrakis, S., andHenin, C., 1974. The evaluation of risky investments with random timing of cash returns.Management Science,21 (1): 79–86.Google Scholar
  10. [10]
    Perrakis, S., andSahin, I., 1976. On risky investments with random timing of cash returns and fixed planning horizon.Management Science,22 (7): 799–809.Google Scholar
  11. [11]
    Barnes, J.W. andZinn, C.D. andEldred, 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.Google Scholar
  12. [12]
    Young, D. andContreras, L.E., 1975. Expected present worths of cash flows under uncertain timing.The Engineering Economist,20 (4): 257–268.Google Scholar
  13. [13]
    Joiner, B.L. andRosenblatt, J.R., 1971. Some properties of the range in samples from Tukey's symmetric Lambda distributions.JASA,66: 394–399.Google Scholar
  14. [14]
    Feller, W., 1966.An introduction to probability theory and its applications. Vol II, John Wiley & Sons, Inc., New York.Google Scholar
  15. [15]
    Bellman, R.E. andRoth, R.S., 1984.The Laplace transform. World Scientific Publishing Co Pte Ltd.Google Scholar
  16. [16]
    Fleischer, G.A., 1981. Assessing the relative efficacy of the transform method for discounting periodic cash flows. 1981ASEE annual conference proceedings, 71–74.Google Scholar
  17. [17]
    Gurnani, C., 1982. Present worth analysis of deterministic periodic cash flows.The Engineering Economist,27 (2): 101–126.Google Scholar
  18. [18]
    Beenhakker, H.L., 1975. Sensitivity analysis of the present value of a project.The Engincering Economist,20 (2): 123–149.Google Scholar
  19. [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. [20]
    Almond, B. andRemer, D.S., 1979. Models for present-worth analysis of selected industrial cash flow patterns.Engineering and Process Economics,4: 455–466.Google Scholar
  21. [21]
    Spiegel, M.R., 1965.Schaum's outline of theory and problems of Laplace transforms. McGraw-Hill Inc., New York.Google Scholar
  22. [22]
    Miller, M.K. andGuy, W.T., 1966. Numerical inversion of the Laplace transform by use of Jacobi polynomials.SIAM Journal on Numerical Analysis,3 (4): 624–635.Google Scholar
  23. [23]
    Crump, K.S., 1976. Numerical inversion of Laplace transforms using a Fourier series approximation.Journal of the Association for Computing Machinery,23 (4): 89–96.Google Scholar
  24. [24]
    Hosono, T., 1981. Numerical inversion of Laplace transform and some applications to wave optics.Radio Science,16 (6): 1015–1019.Google Scholar
  25. [25]
    Buser, S.A., 1986. Laplace transforms as present value rules: A note.The Journal of Finance, Vol. XLI, No. 1: 243–247.Google Scholar
  26. [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. [27]
    Levi, E., 1961. Problemi di ritardo in matematica finanziaria,Giornale Istituto Italiano Attuari: 194–202.Google Scholar
  28. [28]
    Malaska, P. andKinnunen, T., 1986. A model of management goal setting and its dissipative structure.European Journal of Operational Research,25: 75–84.Google Scholar
  29. [29]
    Churchill, R.V., 1958.Operational Mathematics, McGraw-Hill Inc., New York.Google Scholar
  30. [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.Google Scholar
  31. [31]
    Mullineux, N., andReed, J.R. andRichardson, R.G., 1973. Multi-dimensional Laplace transforms and non-linear problems.Int. J. Elect. Enging. Educ.,11: 5–17.Google Scholar
  32. [32]
    Dasarathy, B.V., 1971. D-transforms and non-linear systems analysis.Journal of Sound and Vibration,15 (2): 269–273.Google Scholar
  33. [33]
    Koh, E.L., 1975. Association of variables in n-dimensional Laplace transform.Int. J. Systems Sci. 6 (2): 127–131.Google Scholar
  34. [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. [35]
    Lubbock, J.K. andBansal, V.S., 1969. Multidimensional Laplace transforms for solution of nonlinear equations.Proc. IEE,116 (12): 2075–2082.Google Scholar
  36. [36]
    Joshi, S.G. andSrinivasan, 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.Google Scholar
  37. [37]
    Bussgang, J.J. andEhrman, L. andGraham, 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. [38]
    Karmakar, S.B., 1980. Approximate analysis of non-linear systems by Laplace transform.Journal of Sound and Vibration,69 (4): 597–602.Google Scholar
  39. [39]
    Sato, H. andAsada, K., 1988. Laplace transform transient analysis of a non-linear system.Journal of Sound and Vibration,121 (3): 473–479.Google Scholar
  40. [40]
    Srinivasan, S.K. andGopalan, 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.Google Scholar
  41. [41]
    Smith, D.R., 1978. Optimal repair of a series system.Operations Research,26 (4): 653–662.Google Scholar
  42. [42]
    Takaragi, K. et al., 1985. A probability bound estimation method in Markov reliability analysis.IEEE Transactions on Reliability,R-34 (3): 257–261.Google Scholar
  43. [43]
    Wells, C.E., 1985. An adaptive estimation procedure using the Laplace transformation.IIE Transactions,17 (3): 242–251.Google Scholar
  44. [44]
    Shanthikumar, J.G., 1986. First failure time of dependent parallel systems with safety periods.Microelectronics and Reliability,26 (5): 955–972.Google Scholar
  45. [45]
    Gopalan, M.N. andNagarwalla, H.E., 1986. Cost-benefit analysis of a 1 out ofn: G system with variable repair and preventive maintenance rates.International Journal of Quality & Reliability Management,3 (3): 26–32.Google Scholar
  46. [46]
    Brockett, P.L. andGolden, L.L., 1987. A class of utility functions containing all the common utility functions.Management Science,33 (8): 955–964.Google Scholar
  47. [47]
    Vallée, R. andNicolau E., 1983. Econometric models and generalized Laplace transforms.Econ. Comput. Econ. Cybern. Stud. Res.,18 (4): 79–82.Google Scholar
  48. [48]
    Grubbström, R.W. andLundquist, J., 1975.Theory of Relatively closed systems and applications. Production-Economic Research in Linköping, Profil 2, Linköping.Google Scholar
  49. [49]
    Grubbström, R.W., 1980. A principle for determining the correct capital costs of work-inprogress and inventory.Int. J. Prod. Res.,18 (2): 259–271.Google Scholar
  50. [50]
    Gurnani, C., 1983. Economic analysis of inventory systems.Ind. J. Prod. Res.,21 (2): 261–277.Google Scholar
  51. [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, Elsivier, Amsterdam: 539–561.Google Scholar
  52. [52]
    Asbjørnsen, O.A., 1983. Project evaluation and cash flow forecasting by stochastic simulation.Modeling, Identification and Control,4 (4): 237–254.Google Scholar
  53. [53]
    Williams, J., 1973.Laplace transforms. George Allen & Unwin Ltd.Google Scholar
  54. [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.Google Scholar
  55. [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. [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. [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. [58]
    Grubbström, R.W., andLundquist, J., 1977. The Axsäter integrated production-inventory model interpreted in terms of the theory of relatively closed systems,Journal of Cybernetics,7: 49–67.Google Scholar
  59. [59]
    Grubbström, R.W. andThorstenson, 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.Google Scholar
  60. [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. [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. [62]
    Sivazlian, B.D., 1979. Approximate optimal solution for a D-policy in an M/G/1 queuing system.AIIE Transactions,11 (4): 341–343.Google Scholar
  63. [63]
    Kotiah, T.C.T., 1978. Approximate transient analysis of some queuing systems.Operations Research,26 (2): 333–346.Google Scholar
  64. [64]
    Harrison, J.M., 1975. A priority queue with discounted linear costs.Operations Research,23 (2): 260–269.Google Scholar
  65. [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. [66]
    Doyon, L.R., 1981. Stochastic modeling of facility security-systems for analytical solutions.Computers & Industrial Engineering,5 (2): 127–138.Google Scholar
  67. [67]
    Gibley, R.A. andSundstrom, R., 1975. Some important applications of Laplace transforms.Proceedings of the American Institute for Decision Sciences, P.93.Google Scholar
  68. [68]
    Grubbström, R.W. andJiang, 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. [69]
    Terborgh, G., 1949.Dynamic equipment policy, New York.Google Scholar

Copyright information

© Springer-Verlag 1989

Authors and Affiliations

  • Robert W. Grubbström
    • 1
  • Jiang Yinzhong
    • 2
  1. 1.Department of Production EconomicsLinköping Institute of TechnologyLinköpingSweden
  2. 2.Department of ManagementBeijing Institute of Light IndustryBeijingP.R. of China

Personalised recommendations