AM  Vol.11 No.2 , February 2020
A Note on Laplace Transforms of Some Common Distributions Used in Counting Processes Analysis
Abstract: An important problem of actuarial risk management is the calculation of the probability of ruin. Using probability theory and the definition of the Laplace transform one obtains expressions, in the classical risk model, for survival probabilities in a finite time horizon. Then explicit solutions are found with the inversion of the double Laplace transform; using algebra, the Laplace complex inversion formula and Matlab, for the exponential claim amount distribution.
Cite this paper: Kouassi, E. , Akpata, E. and Pokou, K. (2020) A Note on Laplace Transforms of Some Common Distributions Used in Counting Processes Analysis. Applied Mathematics, 11, 67-75. doi: 10.4236/am.2020.112007.

[1]   Garcia, J.M.A. (2005) Explicit Solutions for Survival Probabilities in the Classical Risk Model. ASTIN Bulletin, 35, 113-130.

[2]   Bhullar, M.S. (2018) Study on Properties and Applications of Laplace Transformation: A Review. Pramana Research Journal, 8, 246-251.

[3]   Bracewell, R.N. (2000) The Fourier Transform and Its Applications. 3rd Edition, McGraw-Hill, Boston, MA.

[4]   Davies, B. (2002) Integral Transforms and Their Applications. 3rd Edition, Springer, New York.

[5]   Dyke, P.P.G. (2001) An Introduction to Laplace Transforms and Fourier Series. Springer, London.

[6]   Feller, W. (1971) An Introduction to Probability Theory and Its Applications. Vol. 2, 2nd Edition, John Wiley and Sons, New York.

[7]   Higgins, J.J. and Keller-McNulty, S. (1995) Concepts in Probability and Stochastic Modeling. Wadsworth Publishing Company, Belmont, CA.

[8]   Jerri, A.J. (1985) Introduction to Integral Equations with Applications. Marcel Dekker, New York.

[9]   Kalbfleisch, J.D. and Prentice, R.L. (2006) The Statistical Analysis of Failure Time Data. Wiley Series in Probability and Statistics.

[10]   Marsden, J.E. and Hoffman, M.J. (1999) Basic Complex Analysis. WH Freeman, New York.

[11]   Ortigueira, M.D., Torres, D.F.M. and Trujillo, J.J. (2016) Exponentials and Laplace Transforms on Non-Uniform Time Scales. Communications in Nonlinear Science and Numerical Simulation, 39, 252-270.

[12]   Parashar, B.P. (2008) Differential and Integral Equations. CBS Publication, New Delhi.

[13]   Reddy, K.J.P. and Vaithyasubramanian, S. (2018) A Survey of Laplace Transform Applications in Various Fields of Science and Engineering. International Journal of Pure and Applied Mathematics, 119, 769-777.

[14]   Ross, S.M. (2007) Introduction to Probability Models. 9th Edition, Academic Press, New York.

[15]   Silverman, R.A. (1974) Complex Analysis with Applications. Prentice Hall, New York.