On the asymptotic behaviour of Lévy processes, Part I: Subexponential and exponential processes

Abstract

We study tail probabilities of the suprema of Lévy processes with subexponential or exponential marginal distributions over compact intervals. Several of the processes for which the asymptotics are studied here for the first time have recently become important to model financial time series. Hence our results should be important, for example, in the assessment of financial risk.CGMY process Esscher transform Exponential distribution Extreme value theory GH process GZ process Infinitely divisible distribution Lévy process Long-tailed distribution Semi-heavy-tailed distribution Subexponential distribution