On the asymptotic behaviour of L\'evy processes, Part I: Subexponential and exponential processes
Journal article, 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
Author
Patrik Albin
Chalmers, Mathematical Sciences, Mathematical Statistics
University of Gothenburg
Mattias Sunden
Chalmers, Mathematical Sciences, Mathematical Statistics
University of Gothenburg
Stochastic Processes and their Applications
0304-4149 (ISSN)
Vol. 119 1 281-304Subject Categories
Probability Theory and Statistics
DOI
10.1016/j.spa.2008.02.004