A Methodology for obtaining the probability density function of the present worth of probabilistic cash flow profiles

Abstract A new approach is presented for analyzing probabilistic cash flow profiles. Integral transform theory is used to obtain a complete analytic characterization of the probability density function of the net present worth of such cash flow profiles. This represents an extension of the current techniques of risk analysis. The methodology includes the usual evaluation and use of the expected value and the second, third and fourth central moments of the density of present worth. However, these descriptive measures do not always provide sufficient information for a complete managerial analysis. The method presented here enables management to fully differentiate between competing investment alternatives using existing methods, such as stochastic dominance, which are based on a knowledge of the form of the associated probability density functions. Simple formulae for evaluating moments of any or all orders are given. Illustrative examples are included to accompany the analytic development for several repre...

[1]  Josef Hadar,et al.  Rules for Ordering Uncertain Prospects , 1969 .

[2]  F. Hillier.  The evaluation of risky interrelated investments , 1966 .

[3]  Walter C. Giffin,et al.  Transform Techniques for Probability Modeling , 1975 .

[4]  Robert W. Grubbström,et al.  On The Application of the Laplace Transform to Certain Economic Problems , 1967 .

[5]  E. Hansen.  A Table of Series and Products , 1977 .

[6]  G. A. Campbell,et al.  Fourier integrals for practical applications , 1931 .

[7]  R. Wooldridge,et al.  Advanced Engineering Mathematics , 1967, The Mathematical Gazette.

[8]  Donovan Young,et al.  Expected Present Worths of Cash Flows Under Uncertain Timing , 1975 .

[9]  J. Quirk,et al.  Admissibility and Measurable Utility Functions , 1962 .

[10]  B. L. Joiner,et al.  Some Properties of the Range in Samples from Tukey's Symmetric Lambda Distributions , 1971 .

[11]  F. Hillier.  THE DERIVATION OF PROBABILISTIC INFORMATION FOR THE EVALUATION OF RISKY INVESTMENTS , 1963 .

[12]  William H. Jean.  Comparison of Moment and Stochastic Dominance Ranking Methods , 1975 .

[13]  Claude G Henin,et al.  The Evaluation of Risky Investments with Random Timing of Cash Returns , 1974 .

[14]  A. Erdélyi,et al.  Tables of integral transforms , 1955 .

[15]  Jose M. A. Tanchoco,et al.  A Closed-Form Methodology for Computing Present Worth Statistics of Risky Discrete Cash-Flows , 1977 .

[16]  William Feller,et al.  An Introduction to Probability Theory and Its Applications , 1951 .

[17]  G. Whitmore,et al.  Third-Degree Stochastic Dominance , 1970 .

[18]  Max K. Miller,et al.  Numerical Inversion of the Laplace Transform by Use of Jacobi Polynomials , 1966 .

[19]  T. W. Hill,et al.  Laplace Transforms for the Economic Analysis of Deterministic Problems in Engineering , 1971 .

[20]  Frederick S. Hillier.  Communications to the Editor—Supplement to “The Derivation of Probabilistic Information for the Evaluation of Risky Investments” , 1965 .

[21]  Harvey Dubner,et al.  Numerical Inversion of Laplace Transforms by Relating Them to the Finite Fourier Cosine Transform , 1968, JACM.

[22]  Haim Levy,et al.  A Note on Portfolio Selection and Investors' Wealth , 1971, Journal of Financial and Quantitative Analysis.

[23]  Kenny S. Crump,et al.  Numerical Inversion of Laplace Transforms Using a Fourier Series Approximation , 1976, J. ACM.

[24]  P. R. Nelson.  The algebra of random variables , 1979 .

[25]  James R. Buck,et al.  Additions to the Laplace Transform Methodology for Economic Analysis , 1975 .

[26]  Athanasios Papoulis,et al.  Probability, Random Variables and Stochastic Processes , 1965 .

[27]  B. Motazed,et al.  A Probabilistic Approach to Risk Analysis in Capital Investment Projects , 1977 .

[28]  B. Wagle,et al.  A Statistical Analysis of Risk in Capital Investment Projects , 1967 .

[29]  Emanuel Parzen,et al.  Modern Probability Theory And Its Applications , 1962 .

[30]  A. Reisman,et al.  Stochastic Cash Flow Formulae Under Conditions of Inflation , 1972 .