2013
On the accuracy of phase-type approximations of heavy-tailed risk models.
Publication
Publication
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 specific 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 prespecified 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.
Additional Metadata | |
---|---|
Null option (theme 11) | |
Scandinavian University Press | |
Scandinavian Actuarial Journal | |
Organisation | Stochastics |
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.
|