Numerical evaluation of ruin probabilities in the classical risk model is an important problem. If claim sizes are heavy-tailed, then such evaluations are challenging. To overcome this, an attractive way is to approximate the claim sizes with a phase-type distribution. What is not clear though is how many phases are enough in order to achieve a specifi c accuracy in the approximation of the ruin probability. The goals of this paper are to investigate the number of phases required so that we can achieve a prespecifi ed accuracy for the ruin probability and to provide error bounds. Also, in the special case of a completely monotone claim size distribution we develop an algorithm to estimate the ruin probability by approximating the excess claim size distribution with a hyperexponential one. Finally, we compare our approximation with the heavy traffic and heavy tail approximations.
Null option (theme 11)
Scandinavian University Press
Scandinavian Actuarial Journal

Vatamidou, E, Adan, I.J.B.F, Vlasiou, M, & Zwart, A.P. (2013). On the accuracy of phase-type approximations of heavy-tailed risk models. Scandinavian Actuarial Journal.