Uniform Asymptotics for Compound Poisson Processes with Regularly\n Varying Jumps and Vanishing Drift

2015/10/23 by Bart Kamphorst, Bert Zwart, Kamphorst, Bart +1
Decision Sciences · Economics, Econometrics and Finance · Mathematics · #FOS: Mathematics #Probability (math.PR) #Probability and Risk Models #Stochastic processes and financial applications #Stochastic processes and statistical mechanics

paper · pdf · doi:10.48550/arxiv.1510.06955

openalex publication_date 2015/10/23 · openalex created_date 2025/10/24 · openalex updated_date 2026/07/28

Abstract

This paper addresses heavy-tailed large deviation estimates for the\ndistribution tail of functionals of a class of spectrally one-sided L 'evy\nprocess. Our contribution is to show that these estimates remain valid in a\nnear-critical regime. This complements recent similar results that have been\nobtained for the all-time supremum of such processes. Specifically, we consider\nlocal asymptotics of the all-time supremum, the supremum of the process until\nexiting [0,\∞), the maximum jump until that time, and the time it takes\nuntil exiting [0,\∞). The proofs rely, among other things, on properties\nof scale functions.\n

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