On the asymptotic behaviour of L\'evy processes, Part I: Subexponential and exponential processes
Artikel i vetenskaplig tidskrift, 2009

We study tail probabilities of suprema of L\'evy 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.

Extreme value theory

Exponential distribution

GZ process

Infinitely divisible distribution

GH process

Esscher transform

CGMY process

Long-tailed distribution

Lévy process

Subexponential distribution

Semi-heavy-tailed distribution

Författare

Patrik Albin

Chalmers, Matematiska vetenskaper, matematisk statistik

Göteborgs universitet

Mattias Sunden

Chalmers, Matematiska vetenskaper, matematisk statistik

Göteborgs universitet

Stochastic Processes and their Applications

0304-4149 (ISSN)

Vol. 119 281-304

Ämneskategorier

Sannolikhetsteori och statistik

DOI

10.1016/j.spa.2008.02.004