General Draw-Down Times for Refracted Spectrally Negative Lévy Processes

Xuan Huang and Jieming Zhou ()
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Xuan Huang: Hunan Normal University
Jieming Zhou: Hunan Normal University

Methodology and Computing in Applied Probability, 2022, vol. 24, issue 2, 875-891

Abstract: Abstract In this paper, we prove several results involving a general draw-down time from the running maximum for refracted spectrally negative Lévy processes. Using an approximation method, which is excursion theory at its heart, we find expressions for the Laplace transforms for the two-sided exit problems which are related to the draw-down time and an expression for the associated potential measure. The results are expressed in terms of scale functions.

Keywords: Refracted spectrally negative Lévy processes; Draw-down time; Exit problems; Potential measure; 60J25; 60J75 (search for similar items in EconPapers)
Date: 2022
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DOI: 10.1007/s11009-022-09933-6

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