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Poissonian potential measures for Lévy risk models

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  • Landriault, David
  • Li, Bin
  • Wong, Jeff T.Y.
  • Xu, Di

Abstract

This paper studies the potential (or resolvent) measures of spectrally negative Lévy processes killed on exiting (bounded or unbounded) intervals, when the underlying process is observed at the arrival epochs of an independent Poisson process. Explicit representations of these so-called Poissonian potential measures are established in terms of newly defined Poissonian scale functions. Moreover, Poissonian exit measures are explicitly solved by finding a direct relation with Poissonian potential measures. Our results generalize Albrecher et al. (2016) in which Poissonian exit identities are solved. As an application of Poissonian potential measures, we extend the Gerber–Shiu analysis in Baurdoux et al. (2016) to a (more general) Parisian risk model subject to Poissonian observations.

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  • Landriault, David & Li, Bin & Wong, Jeff T.Y. & Xu, Di, 2018. "Poissonian potential measures for Lévy risk models," Insurance: Mathematics and Economics, Elsevier, vol. 82(C), pages 152-166.
    • Handle: RePEc:eee:insuma:v:82:y:2018:i:c:p:152-166
    DOI: 10.1016/j.insmatheco.2018.07.004
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    References listed on IDEAS

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    3. Lkabous, Mohamed Amine & Wang, Zijia, 2023. "On the area in the red of Lévy risk processes and related quantities," Insurance: Mathematics and Economics, Elsevier, vol. 111(C), pages 257-278.
    4. Lkabous, Mohamed Amine, 2019. "A note on Parisian ruin under a hybrid observation scheme," Statistics & Probability Letters, Elsevier, vol. 145(C), pages 147-157.
    5. Sripad Motiram & Vamsi Vakulabharanam, 2020. "Intra-City Inequalities, Neighborhoods and Economic Development," Working Papers 2020-01, University of Massachusetts Boston, Economics Department.
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    7. Mohamed Amine Lkabous, 2019. "A note on Parisian ruin under a hybrid observation scheme," Papers 1907.09993, arXiv.org.

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