The exact asymptotics for hitting probability of a remote orthant by a multivariate L\'evy process: the Cram\'er case
Abstract
For a multivariate L\'evy process satisfying the Cram\'er moment condition and having a drift vector with at least one negative component, we derive the exact asymptotics of the probability of ever hitting the positive orthant that is being translated to infinity along a fixed vector with positive components. This problem is motivated by the multivariate ruin problem introduced in F. Avram et al. (2008) in the two-dimensional case. Our solution relies on the analysis from Y. Pan and K. Borovkov (2017) for multivariate random walks and an appropriate time discretization.
Cite
@article{arxiv.1802.06577,
title = {The exact asymptotics for hitting probability of a remote orthant by a multivariate L\'evy process: the Cram\'er case},
author = {Konstantin Borovkov and Zbigniew Palmowski},
journal= {arXiv preprint arXiv:1802.06577},
year = {2018}
}
Comments
7 pages, 0 figures. In the new version we fixed a bug present in the original one (the value of the constant in the main result proved to be different from the originally claimed)