A Drawdown Reflected Spectrally Negative Lévy Process

Wenyuan Wang () and Xiaowen Zhou ()
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Wenyuan Wang: Xiamen University
Xiaowen Zhou: Concordia University

Journal of Theoretical Probability, 2021, vol. 34, issue 1, 283-306

Abstract: Abstract In this paper, we study a spectrally negative Lévy process that is reflected at its drawdown level whenever a drawdown time from the running supremum arrives. Using an excursion-theoretical approach, for such a reflected process we find the Laplace transform of the upper exiting time and an expression of the associated potential measure. When the reflected process is identified as a risk process with capital injections, the expected total amount of discounted capital injections prior to the exiting time and the Laplace transform of the accumulated capital injections until the exiting time are also obtained. The results are expressed in terms of scale functions for the spectrally negative Lévy process.

Keywords: Spectrally negative Lévy process; Reflected process; Drawdown time; Potential measure; Excursion theory; Risk process; Capital injection; Primary 60G51; Secondary 60E10; 60J35 (search for similar items in EconPapers)
Date: 2021
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Citations: View citations in EconPapers (3)

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DOI: 10.1007/s10959-019-00971-4

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