Exit problems for general draw-down times of spectrally negative Lévy processes
Abstract
For spectrally negative Lévy 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 Lévy processes.
- Publication:
-
arXiv e-prints
- Pub Date:
- February 2017
- DOI:
- 10.48550/arXiv.1702.07259
- arXiv:
- arXiv:1702.07259
- Bibcode:
- 2017arXiv170207259L
- Keywords:
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- Mathematics - Probability;
- 60G51;
- 60E10;
- 60J35