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General Draw-Down Times for Refracted Spectrally Negative Lévy Processes

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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.

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Authors and Affiliations

  1. MOE-LCSM, School of Mathematics and Statistics, Hunan Normal University, Changsha, Hunan, 410081, P.R. China

    Xuan Huang & Jieming Zhou

  2. Key Laboratory of Applied Statistics and Data Science, School of Mathematics and Statistics, Hunan Normal University, College of Hunan Province, Changsha, Hunan, 410081, P.R. China

    Jieming Zhou

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  1. Xuan Huang
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  2. Jieming Zhou
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Correspondence to Jieming Zhou.

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This work is supported by the grants from the Natural Science Foundation of Hunan Province(No. 2021JJ30436), and the Scientific Research Fund of Hunan Provincial Education Department, China (Nos. 19B343,20B381,20K084), and the Changsha Municipal Natural Science Foundation (No. kq2014072).

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Huang, X., Zhou, J. General Draw-Down Times for Refracted Spectrally Negative Lévy Processes. Methodol Comput Appl Probab 24, 875–891 (2022). https://doi.org/10.1007/s11009-022-09933-6

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  • DOI: https://doi.org/10.1007/s11009-022-09933-6

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