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A Note on Laplace Transforms of Some Common Distributions Used in Counting Processes Analysis
Department of Economics, University of the Western Cape, Cape Town, South Africa
Department of Mathematics, University Felix Houphouet Boigny, Abidjan, Cote d’Ivoire
Department of Economics, University Felix Houphouet Boigny, Abidjan, Cote d’Ivoire
- 1 Department of Economics, University of the Western Cape, Cape Town, South Africa
- 2 Department of Mathematics, University Felix Houphouet Boigny, Abidjan, Cote d’Ivoire
- 3 Department of Economics, University Felix Houphouet Boigny, Abidjan, Cote d’Ivoire
Applied Mathematics·Volume 11 (2020)·Pages 67–75·Published 20 January 2020·DOI10.4236/am.2020.112007
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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.
KeywordsLaplace TransformsCommon DistributionsAnalysisProbability DistributionsCounting Processes
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