Tail expansions for the distribution of the maximum of a random walk with negative drift and regularly varying increments

Details Tail expansions for the distribution of the maximum of a random walk with negative drift and regularly varying increments Tail expansions for the distribution of the maximum of a random walk with negative drift and regularly varying increments

2006-04-18

arxiv.org/abs/math/0604377v1

Mathematics

Probability

16 pages

Scientific paper

Let F be a distribution function with negative mean and regularly varying
right tail. Under a mild smoothness condition we derive higher order asymptotic
expansions for the tail distribution of the maxima of the random walk generated
by F. An application to ruin probabilities is developed.

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