On moments based Padé approximations of ruin probabilities

In this paper, we investigate the quality of the moments based Padé 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 Padé approximation, orthogonal polynomials, and Gaussian quadrature. These connections may turn out useful for providing rates of convergence.