Title

Asymptotic Distributions of the Overshoot and Undershoots for the Lévy Insurance Risk Process in the Cramér and Convolution Equivalent Cases

Author(s)/Creator(s)

Philip S. Griffin, Syracuse University
Ross A. Maller, Australian National University
Kees van Schaik, University of Manchester

Document Type

Article

Date

6-12-2011

Disciplines

Mathematics

Description/Abstract

Recent models of the insurance risk process use a Levy process to generalise the traditional Cramer-Lundberg compound Poisson model. This paper is concerned with the behaviour of the distributions of the overshoot and undershoots of a high level, for a Levy process which drifts to -infinity and satis es a Cramer or a convolution equivalent condition. We derive these asymptotics under minimal conditions in the Cramer case, and compare them with known results for the convolution equivalent case, drawing attention to the striking and unexpected fact that they become identical when certain parameters tend to equality. Thus, at least regarding these quantities, the "medium-heavy" tailed convolution equivalent model segues into the "light-tailed" Cramer model in a natural way. This suggests a usefully expanded exibility for modelling the insurance risk process. We illustrate this relationship by

comparing the asymptotic distributions obtained for the overshoot and undershoots, assuming the Levy process belongs to the "GTSC" class.

Additional Information

This manuscript is from arXiv.org, for more information see http://arxiv.org/abs/1106.3292

Recommended Citation

Griffin, Philip S.; Maller, Ross A.; and van Schaik, Kees, "Asymptotic Distributions of the Overshoot and Undershoots for the Lévy Insurance Risk Process in the Cramér and Convolution Equivalent Cases" (2011). Mathematics - All Scholarship. 94.
https://surface.syr.edu/mat/94

Source

Harvested from arXiv.org