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Occupation times of intervals until first passage times for spectrally negative Lévy processes

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  • Loeffen, Ronnie L.
  • Renaud, Jean-François
  • Zhou, Xiaowen

Abstract

In this paper, we identify Laplace transforms of occupation times of intervals until first passage times for spectrally negative Lévy processes. New analytical identities for scale functions are derived and therefore the results are explicitly stated in terms of the scale functions of the process. Applications to option pricing and insurance risk models are also presented.

Suggested Citation

  • 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.
    • Handle: RePEc:eee:spapps:v:124:y:2014:i:3:p:1408-1435
    DOI: 10.1016/j.spa.2013.11.005
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    References listed on IDEAS

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    1. Loeffen, R.L., 2009. "An optimal dividends problem with transaction costs for spectrally negative Lévy processes," Insurance: Mathematics and Economics, Elsevier, vol. 45(1), pages 41-48, August.
    2. 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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