Software for an implementation of Weeks' method for the inverse Laplace transform
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ASMTA '09 Proceedings of the 16th International Conference on Analytical and Stochastic Modeling Techniques and Applications
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In this paper, we investigate the quality of the moments based Pade approximation of ultimate ruin probabilities by exponential mixtures. We present several numerical examples illustrating the quick convergence of the method in the case of Gamma processes. While this is not surprising in the completely monotone case (which holds when the shape parameter is less than 1), it is more so in the opposite case, for which we improve even further the performance by a fix-up which may be of special importance due to its potential use in the four moments Gamma approximation. We also review the connection of the exponential mixtures approximation to Pade approximation, orthogonal polynomials, and Gaussian quadrature. These connections may turn out useful for providing rates of convergence.