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Subexponential Distributions — Large Deviations with Applications to Insurance and Queueing Models

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Summary

This paper presents a fine large-deviations theory for heavy-tailed distributions whose tails are heavier than exp(−√t and have finite second moment. Asymptotics for first passage times are derived. The results are applied to estimate the finite time ruin probabilities in insurance as well as the busy period in a GI/G/1 queueing model.
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Keywords: Baxter—Spitzer identity; busy period; finite time ruin probability; first passage times; insurance; large deviations; queueing theory; subexponential distributions; transient random walk

Document Type: Research Article

Affiliations: 1: Institute of Mathematics and Informatics, Lithuania 2: Center for Mathematical Sciences, Munich University of Technology, Germany

Publication date: March 1, 2004

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