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Occupation Times of Intervals Until Last Passage Times for Spectrally Negative Lévy Processes

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  • Chunhao Cai

    (Nankai University)

  • Bo Li

    (Nankai University)

Abstract

In this paper, we derive the Laplace transform of occupation times of intervals until last passage times for spectrally negative Lévy processes. Motivated by [2], the last passage times before an independent exponential variable are investigated. By a dual argument, explicit formulas are obtained and expressed as a modified version of the analytical identities introduced in Loeffen et al. [13]. As an application, a corridor option and an Omega risk model are studied here.

Suggested Citation

  • Chunhao Cai & Bo Li, 2018. "Occupation Times of Intervals Until Last Passage Times for Spectrally Negative Lévy Processes," Journal of Theoretical Probability, Springer, vol. 31(4), pages 2194-2215, December.
    • Handle: RePEc:spr:jotpro:v:31:y:2018:i:4:d:10.1007_s10959-017-0782-0
    DOI: 10.1007/s10959-017-0782-0
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    References listed on IDEAS

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    1. Gerber, Hans U., 1990. "When does the surplus reach a given target?," Insurance: Mathematics and Economics, Elsevier, vol. 9(2-3), pages 115-119, September.
    2. 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.
    3. 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.
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    Cited by:

    1. Landriault, David & Li, Bin & Lkabous, Mohamed Amine & Wang, Zijia, 2023. "Bridging the first and last passage times for Lévy models," Stochastic Processes and their Applications, Elsevier, vol. 157(C), pages 308-334.

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