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Two-sided discounted potential measures for spectrally negative Lévy processes

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  • Li, Yingqiu
  • Zhou, Xiaowen
  • Zhu, Na

Abstract

For spectrally negative Lévy processes, we find expressions of potential measures that are discounted by their joint occupation times over semi-infinite intervals (−∞,0) and (0,∞). These expressions are in terms of the associated scale functions and the inverse functions of Laplace exponents.

Suggested Citation

  • Li, Yingqiu & Zhou, Xiaowen & Zhu, Na, 2015. "Two-sided discounted potential measures for spectrally negative Lévy processes," Statistics & Probability Letters, Elsevier, vol. 100(C), pages 67-76.
    • Handle: RePEc:eee:stapro:v:100:y:2015:i:c:p:67-76
    DOI: 10.1016/j.spl.2015.01.022
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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. 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.
    4. 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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    Cited by:

    1. Mohamed Amine Lkabous, 2019. "Poissonian occupation times of spectrally negative L\'evy processes with applications," Papers 1907.09990, arXiv.org.
    2. David Landriault & Bin Li & Mohamed Amine Lkabous, 2019. "On occupation times in the red of L\'evy risk models," Papers 1903.03721, arXiv.org, revised Jul 2019.
    3. Landriault, David & Li, Bin & Lkabous, Mohamed Amine, 2020. "On occupation times in the red of Lévy risk models," Insurance: Mathematics and Economics, Elsevier, vol. 92(C), pages 17-26.
    4. Lan Wu & Jiang Zhou & Shuang Yu, 2017. "Occupation Times of General Lévy Processes," Journal of Theoretical Probability, Springer, vol. 30(4), pages 1565-1604, December.

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