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Moments of the Ruin Time in a Lévy Risk Model

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  • Philipp Lukas Strietzel

    (Technische Universität Dresden)

  • Anita Behme

    (Technische Universität Dresden)

Abstract

We derive formulas for the moments of the ruin time in a Lévy risk model and use these to determine the asymptotic behavior of the moments of the ruin time as the initial capital tends to infinity. In the special case of the perturbed Cramér-Lundberg model with phase-type or even exponentially distributed claims, we explicitly compute the first two moments of the ruin time. All our considerations distinguish between the profitable and the unprofitable setting.

Suggested Citation

  • Philipp Lukas Strietzel & Anita Behme, 2022. "Moments of the Ruin Time in a Lévy Risk Model," Methodology and Computing in Applied Probability, Springer, vol. 24(4), pages 3075-3099, December.
    • Handle: RePEc:spr:metcap:v:24:y:2022:i:4:d:10.1007_s11009-022-09967-w
    DOI: 10.1007/s11009-022-09967-w
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    References listed on IDEAS

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    1. Wing Yan Lee & Gordon E. Willmot, 2016. "The moments of the time to ruin in dependent Sparre Andersen models with Coxian claim sizes," Scandinavian Actuarial Journal, Taylor & Francis Journals, vol. 2016(6), pages 550-564, July.
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    8. Drekic, Steve & Stafford, James E. & Willmot, Gordon E., 2004. "Symbolic calculation of the moments of the time of ruin," Insurance: Mathematics and Economics, Elsevier, vol. 34(1), pages 109-120, February.
    9. Lin, X. Sheldon & Willmot, Gordon E., 2000. "The moments of the time of ruin, the surplus before ruin, and the deficit at ruin," Insurance: Mathematics and Economics, Elsevier, vol. 27(1), pages 19-44, August.
    10. Tsai, Cary Chi-Liang & Willmot, Gordon E., 2002. "On the moments of the surplus process perturbed by diffusion," Insurance: Mathematics and Economics, Elsevier, vol. 31(3), pages 327-350, December.
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    12. Pitts, Susan M. & Politis, Konstadinos, 2008. "Approximations for the moments of ruin time in the compound Poisson model," Insurance: Mathematics and Economics, Elsevier, vol. 42(2), pages 668-679, April.
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    1. 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.

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