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

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

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 a...

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Veröffentlicht in:Australian & New Zealand journal of statistics 2004-03, Vol.46 (1), p.145-154
Hauptverfasser: Baltrūnas, Aleksandras, Klüppelberg, Claudia
Format: Artikel
Sprache:eng
Schlagworte:
Baxter-Spitzer identity
busy period
Economic theory
finite time ruin probability
first passage times
Identity
Insurance
large deviations
Probability
queueing theory
Statistical methods
subexponential distributions
transient random walk
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Zusammenfassung: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.
ISSN:1369-1473
1467-842X
DOI:10.1111/j.1467-842X.2004.00320.x