For a random walk with negative drift we study the exceedance
probability (ruin probability) of a high threshold. The steps of this walk
(claim sizes) constitute a stationary ergodic stable process. We study how ruin
occurs in this situation and evaluate the asymptotic behavior of the ruin
probability for a large variety of stationary ergodic stable processes. Our
findings show that the order of magnitude of the ruin probability varies
significantly from one model to another. In particular, ruin becomes much more
likely when the claim sizes exhibit long-range dependence. The proofs exploit
large deviation techniques for sums of dependent stable random variables and
the series representation of a stable process as a function of a Poisson
process.
Publié le : 2000-10-14
Classification:
Stable process,
stationary process,
ruin probability,
heavy tails,
supremum,
negative drift,
risk,
60E07,
60G10,
60K30
@article{1019160509,
author = {Mikosch, Thomas and Samorodnitsky, Gennady},
title = {Ruin probability with claims modeled by a stationary ergodic
stable process},
journal = {Ann. Probab.},
volume = {28},
number = {1},
year = {2000},
pages = { 1814-1851},
language = {en},
url = {http://dml.mathdoc.fr/item/1019160509}
}
Mikosch, Thomas; Samorodnitsky, Gennady. Ruin probability with claims modeled by a stationary ergodic
stable process. Ann. Probab., Tome 28 (2000) no. 1, pp. 1814-1851. http://gdmltest.u-ga.fr/item/1019160509/