On the accuracy of phase-type approximations of heavy-tailed risk models

Abstract

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 pre-specified 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.

arXiv comment24 pages, 13 figures, 8 tables, 38 references

References in corpus (1)

• On the transition from heavy traffic to heavy tails for the M/G/1 queue: The regularly varying case

Cited by in corpus (4)

• Building Mean Field State Transition Models Using The Generalized Linear Chain Trick and Continuous Time Markov Chain Theory
• Corrected phase-type approximations of heavy-tailed risk models using perturbation analysis
• Asymptotic tail behavior of phase-type scale mixture distributions
• Approximation of Ruin Probabilities via Erlangized Scale Mixtures