We consider spectrally negative Lévy process and determine
the joint Laplace transform of the exit time and exit position
from an interval containing the origin of the process reflected
in its supremum. In the literature of fluid models,
this stopping time can be identified
as the time to buffer-overflow.
The Laplace transform is determined in
terms of the scale functions that appear in the two-sided exit problem of
the given Lévy process. The obtained results together
with existing results on two sided exit problems are applied
to solving optimal stopping problems associated with the pricing
of Russian options and their Canadized versions.
@article{1075828052,
author = {Avram, F. and Kyprianou, A. E. and Pistorius, M. R.},
title = {Exit problems for spectrally negative L\'evy processes and applications to (Canadized) Russian options},
journal = {Ann. Appl. Probab.},
volume = {14},
number = {1},
year = {2004},
pages = { 215-238},
language = {en},
url = {http://dml.mathdoc.fr/item/1075828052}
}
Avram, F.; Kyprianou, A. E.; Pistorius, M. R. Exit problems for spectrally negative Lévy processes and applications to (Canadized) Russian options. Ann. Appl. Probab., Tome 14 (2004) no. 1, pp. 215-238. http://gdmltest.u-ga.fr/item/1075828052/