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

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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.

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References

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

    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., 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. 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. Reisman, A. andRao, 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.

    Google Scholar 

  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. 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. 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. 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. 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. 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. 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. 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. andRoth, R.S., 1984.The Laplace transform. World Scientific Publishing Co Pte Ltd.

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

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

    Google Scholar 

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

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

    Google Scholar 

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

    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.

    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.

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

  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. 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.

    Google Scholar 

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

    Google Scholar 

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

    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. andBansal, V.S., 1969. Multidimensional Laplace transforms for solution of nonlinear equations.Proc. IEE,116 (12): 2075–2082.

    Google Scholar 

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

    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.

    Google Scholar 

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

    Google Scholar 

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

    Google Scholar 

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

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

    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, Elsivier, 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.

    Google Scholar 

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

  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. 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.

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

  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.

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

  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/1 queuing system.AIIE Transactions,11 (4): 341–343.

    Google Scholar 

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

    Google Scholar 

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

    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.

    Google Scholar 

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

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

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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

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  1. Robert W. Grubbström
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  2. Jiang Yinzhong
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Grubbström, R.W., Yinzhong, J. A survey and analysis of the application of the Laplace transform to present value problems. Rivista di Matematica per le Scienze Economiche e Sociali 12, 43–62 (1989). https://doi.org/10.1007/BF02085591

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