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

Ph . Barbe; W. P. McCormick; C. Zhang

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

Ph . Barbe·W. P. McCormick·C. Zhang

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Abstract

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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Ph . Barbe, W. P. McCormick, C. Zhang. 2006-04-18. Tail expansions for the distribution of the maximum of a random walk with negative drift and regularly varying increments. https://arxiv.org/abs/math/0604377

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