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

[摘要] 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. The expansion is based on an expansion for the right Wiener-Hopf factor which we derive first. An application to ruin probabilities is developed. (c) 2007 Elsevier B.V. All rights reserved.

[发布日期] 2007-12-01

[关键词] tail expansion;random walk;regularly varying;Wiener-Hopf factor;ruin probability