Exit problems for general draw-down times of spectrally negative L\'evy processes
Probability
2019-07-17 v3
Abstract
For spectrally negative L\'evy processes, we prove several fluctuation results involving a general draw-down time, which is a downward exit time from a dynamic level that depends on the running maximum of the process. In particular, we find expressions of the Laplace transforms for the two-sided exit problems involving the draw-down time. We also find the Laplace transforms for the hitting time and creeping time over the running-maximum related draw-down level, respectively, and obtain an expression for a draw-down associated potential measure. The results are expressed in terms of scale functions for the spectrally negative L\'evy processes.
Cite
@article{arxiv.1702.07259,
title = {Exit problems for general draw-down times of spectrally negative L\'evy processes},
author = {Bo Li and Nhat Linh Vu and Xiaowen Zhou},
journal= {arXiv preprint arXiv:1702.07259},
year = {2019}
}