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

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.