TITLE:
A Note on Laplace Transforms of Some Common Distributions Used in Counting Processes Analysis
AUTHORS:
Eugene Kouassi, Edouard Akpata, Koffi Pokou
KEYWORDS:
Laplace Transforms, Common Distributions, Analysis, Probability Distributions, Counting Processes
JOURNAL NAME:
Applied Mathematics,
Vol.11 No.2,
January
21,
2020
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.