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Laplace Transformation of the Ruin Time for a Risk Model with a Parisian Implementation Delay

Author

Listed:
  • Tao Sun

    (School of Statistics and Data Science, Qufu Normal University, Qufu 273165, China)

  • Xinqiu Zhang

    (School of Mathematical Sciences, Qufu Normal University, Qufu 273165, China)

Abstract

In this paper, we apply the concept of the Parisian implementation delay to dividend payments and assume that the claim amount paid Z i by the insurance company for the i th time follows an exponential distribution. We give the Laplace transformation of the ruin time for a risk model with a Parisian implementation delay and give display expressions using the scale function.

Suggested Citation

  • Tao Sun & Xinqiu Zhang, 2024. "Laplace Transformation of the Ruin Time for a Risk Model with a Parisian Implementation Delay," Mathematics, MDPI, vol. 12(4), pages 1-12, February.
    • Handle: RePEc:gam:jmathe:v:12:y:2024:i:4:p:551-:d:1337597
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    References listed on IDEAS

    as
    1. Avanzi, Benjamin & Gerber, Hans U., 2008. "Optimal Dividends in the Dual Model with Diffusion," ASTIN Bulletin, Cambridge University Press, vol. 38(2), pages 653-667, November.
    2. Gerber, Hans U. & Smith, Nathaniel, 2008. "Optimal dividends with incomplete information in the dual model," Insurance: Mathematics and Economics, Elsevier, vol. 43(2), pages 227-233, October.
    3. Afonso, Lourdes B. & Cardoso, Rui M.R. & Egídio dos Reis, Alfredo D., 2013. "Dividend problems in the dual risk model," Insurance: Mathematics and Economics, Elsevier, vol. 53(3), pages 906-918.
    4. Dassios, Angelos & Wu, Shanle, 2009. "On barrier strategy dividends with Parisian implementation delay for classical surplus processes," Insurance: Mathematics and Economics, Elsevier, vol. 45(2), pages 195-202, October.
    5. 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.
    6. Irmina Czarna & Zbigniew Palmowski & Przemysław Świa̧tek, 2017. "Discrete time ruin probability with Parisian delay," Scandinavian Actuarial Journal, Taylor & Francis Journals, vol. 2017(10), pages 854-869, November.
    7. Eric Cheung & David Landriault & Gordon Willmot & Jae-Kyung Woo, 2010. "Gerber–Shiu analysis with a generalized penalty function," Scandinavian Actuarial Journal, Taylor & Francis Journals, vol. 2010(3), pages 185-199.
    8. Cheung, Eric C.K. & Drekic, Steve, 2008. "Dividend Moments in the Dual Risk Model: Exact and Approximate Approaches," ASTIN Bulletin, Cambridge University Press, vol. 38(2), pages 399-422, November.
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