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Exit problems for general draw-down times of spectrally negative L��vy processes
- Publication Year :
- 2017
- Publisher :
- arXiv, 2017.
-
Abstract
- For spectrally negative L��vy 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��vy processes.
- Subjects :
- 60G51, 60E10, 60J35
Probability (math.PR)
FOS: Mathematics
Subjects
Details
- Database :
- OpenAIRE
- Accession number :
- edsair.doi...........02e66147eef58c901d6351d652ff51ec
- Full Text :
- https://doi.org/10.48550/arxiv.1702.07259