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Occupation times for spectrally negative Lévy processes on the last exit time

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  • Li, Yingqiu
  • Wei, Yushao
  • Peng, Zhaohui

Abstract

In this paper, adopting the Poisson approach and the perturbation approach for spectrally negative Lévy processes (often abbreviated as SNLP), we consider some joint Laplace transforms of the last exit time from two semi-infinite interval, the value of the process, and the associated occupation time. Motivated by Li and Cai (2018), Li et al. (2017), Our results can recover some previous results when taking the limit to infinity in our results.

Suggested Citation

  • Li, Yingqiu & Wei, Yushao & Peng, Zhaohui, 2021. "Occupation times for spectrally negative Lévy processes on the last exit time," Statistics & Probability Letters, Elsevier, vol. 175(C).
    • Handle: RePEc:eee:stapro:v:175:y:2021:i:c:s0167715221000730
    DOI: 10.1016/j.spl.2021.109111
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    References listed on IDEAS

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    1. Li, Yingqiu & Zhou, Xiaowen, 2014. "On pre-exit joint occupation times for spectrally negative Lévy processes," Statistics & Probability Letters, Elsevier, vol. 94(C), pages 48-55.
    2. Dickson, David C.M. & Li, Shuanming, 2013. "The distributions of the time to reach a given level and the duration of negative surplus in the Erlang(2) risk model," Insurance: Mathematics and Economics, Elsevier, vol. 52(3), pages 490-497.
    3. Loeffen, Ronnie L. & Renaud, Jean-François & Zhou, Xiaowen, 2014. "Occupation times of intervals until first passage times for spectrally negative Lévy processes," Stochastic Processes and their Applications, Elsevier, vol. 124(3), pages 1408-1435.
    4. Landriault, David & Renaud, Jean-François & Zhou, Xiaowen, 2011. "Occupation times of spectrally negative Lévy processes with applications," Stochastic Processes and their Applications, Elsevier, vol. 121(11), pages 2629-2641, November.
    5. Ning Cai & Nan Chen & Xiangwei Wan, 2010. "Occupation Times of Jump-Diffusion Processes with Double Exponential Jumps and the Pricing of Options," Mathematics of Operations Research, INFORMS, vol. 35(2), pages 412-437, May.
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