Corrected phase-type approximations of heavy-tailed risk models using perturbation analysis

Abstract

Numerical evaluation of performance measures in heavy-tailed risk models is an important and challenging problem. In this paper, we construct very accurate approximations of such performance measures that provide small absolute and relative errors. Motivated by statistical analysis, we assume that the claim sizes are a mixture of a phase-type and a heavy-tailed distribution and with the aid of perturbation analysis we derive a series expansion for the performance measure under consideration. Our proposed approximations consist of the first two terms of this series expansion, where the first term is a phase-type approximation of our measure. We refer to our approximations collectively as corrected phase-type approximations. We show that the corrected phase-type approximations exhibit a nice behavior both in finite and infinite time horizon, and we check their accuracy through numerical experiments.

24 pages, 2 tables, 1 figure, 41 references

References in corpus (4)

• Ruin Probabilities and Overshoots for General Levy Insurance Risk Processes
• Ruin probabilities and decompositions for general perturbed risk processes
• On the accuracy of phase-type approximations of heavy-tailed risk models
• On the transition from heavy traffic to heavy tails for the M/G/1 queue: The regularly varying case

Cited by in corpus (5)

• Asymptotic tail behavior of phase-type scale mixture distributions
• Corrected phase-type approximations for the workload of the MAP/G/1 queue with heavy-tailed service times
• Approximation of Ruin Probabilities via Erlangized Scale Mixtures
• Corrected phase-type approximations of heavy-tailed queueing models in a Markovian environment
• Phase-type approximations perturbed by a heavy-tailed component for the Gerber-Shiu function of risk processes with two-sided jumps