On moments based Padé approximations of ruin probabilities
F. Avram, D.F. Chedom, and A. Horváth
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.