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Some Expressions of a Generalized Version of the Expected Time in the Red and the Expected Area in Red

Author

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  • Julien Callant

    (Université Libre de Bruxelles (ULB))

  • Julien Trufin

    (Université Libre de Bruxelles (ULB))

  • Pierre Zuyderhoff

    (Université Libre de Bruxelles (ULB))

Abstract

In this paper, we study a generalized version of the expected time in the red and the expected area in red introduced in Loisel (2005). We derive some expressions for this risk measure both in light tailed and heavy tailed cases for general risk processes. Then, some further expressions are obtained for Lévy processes together with an upper bound in the light-tailed case and an additional result for large initial capitals in the subexponential case.

Suggested Citation

  • Julien Callant & Julien Trufin & Pierre Zuyderhoff, 2022. "Some Expressions of a Generalized Version of the Expected Time in the Red and the Expected Area in Red," Methodology and Computing in Applied Probability, Springer, vol. 24(2), pages 595-611, June.
    • Handle: RePEc:spr:metcap:v:24:y:2022:i:2:d:10.1007_s11009-021-09915-0
    DOI: 10.1007/s11009-021-09915-0
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    References listed on IDEAS

    as
    1. Stéphane Loisel, 2005. "Differentiation of some functionals of risk processes and optimal reserve allocation," Post-Print hal-00397289, HAL.
    2. Loisel, Stéphane & Trufin, Julien, 2014. "Properties of a risk measure derived from the expected area in red," Insurance: Mathematics and Economics, Elsevier, vol. 55(C), pages 191-199.
    3. Stéphane Loisel, 2005. "Differentiation of functionals of risk processes and optimal reserve allocation," Post-Print hal-00397290, HAL.
    4. Stéphane Loisel, 2005. "Differentiation of some functionals of risk processes," Post-Print hal-00157739, HAL.
    5. Stéphane Loisel, 2005. "Differentiation of some functionals of multidimensional risk processes and determination of optimal reserve allocation," Post-Print hal-00397287, HAL.
    6. Macci, Claudio, 2008. "Large deviations for the time-integrated negative parts of some processes," Statistics & Probability Letters, Elsevier, vol. 78(1), pages 75-83, January.
    7. Romain Biard & Stéphane Loisel & Claudio Macci & Noel Veraverbeke, 2010. "Asymptotic behavior of the finite-time expected time-integrated negative part of some risk processes and optimal reserve allocation," Post-Print hal-00372525, HAL.
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    Cited by:

    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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