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A Note on a Modified Parisian Ruin Concept

Author

Listed:
  • Eric C. K. Cheung

    (School of Risk and Actuarial Studies, UNSW Business School, University of New South Wales, Sydney, NSW 2052, Australia)

  • Jeff T. Y. Wong

    (Department of Statistics and Actuarial Science, The University of Hong Kong, Pokfulam Road, Hong Kong)

Abstract

Traditionally, Parisian ruin is said to occur when the insurer’s surplus process has stayed below level zero continuously for a certain grace period. Inspired by this concept, in this paper we propose a modification by assuming that once a grace period has been granted when the surplus becomes negative, the surplus level will not be monitored continuously in the interim, but instead it will be checked at the end of the grace period to see whether the business has recovered. Under an Erlang distributed grace period, a computationally tractable formula for the Gerber–Shiu expected discounted penalty function is derived. Numerical examples regarding the modified Parisian ruin probability are also provided.

Suggested Citation

  • Eric C. K. Cheung & Jeff T. Y. Wong, 2023. "A Note on a Modified Parisian Ruin Concept," Risks, MDPI, vol. 11(3), pages 1-15, March.
    • Handle: RePEc:gam:jrisks:v:11:y:2023:i:3:p:56-:d:1092842
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    References listed on IDEAS

    as
    1. Albrecher, Hansjörg & Ivanovs, Jevgenijs, 2017. "Strikingly simple identities relating exit problems for Lévy processes under continuous and Poisson observations," Stochastic Processes and their Applications, Elsevier, vol. 127(2), pages 643-656.
    2. Hansjörg Albrecher & Jevgenijs Ivanovs, 2013. "A Risk Model with an Observer in a Markov Environment," Risks, MDPI, vol. 1(3), pages 1-14, November.
    3. Loeffen, R. & Palmowski, Z. & Surya, B.A., 2018. "Discounted penalty function at Parisian ruin for Lévy insurance risk process," Insurance: Mathematics and Economics, Elsevier, vol. 83(C), pages 190-197.
    4. Bin Li & Qihe Tang & Lihe Wang & Xiaowen Zhou, 2014. "Liquidation risk in the presence of Chapters 7 and 11 of the US bankruptcy code," Journal of Financial Engineering (JFE), World Scientific Publishing Co. Pte. Ltd., vol. 1(03), pages 1-19.
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