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Moments of the Surplus before Ruin and the Deficit at Ruin in the Erlang(2) Risk Process

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  • Yebin Cheng
  • Qihe Tang

Abstract

This paper investigates the moments of the surplus before ruin and the deficit at ruin in the Erlang(2) risk process. Using the integro-differential equation that we establish, we obtain some explicit expressions for the moments. Furthermore, when the claim size is exponentially and subexponentially distributed, asymptotic relationships for the moments are derived as the initial capital tends to infinity. Also, we show the joint probability density function of the surplus before ruin and the deficit at ruin.

Suggested Citation

  • Yebin Cheng & Qihe Tang, 2003. "Moments of the Surplus before Ruin and the Deficit at Ruin in the Erlang(2) Risk Process," North American Actuarial Journal, Taylor & Francis Journals, vol. 7(1), pages 1-12.
    • Handle: RePEc:taf:uaajxx:v:7:y:2003:i:1:p:1-12
    DOI: 10.1080/10920277.2003.10596073
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    Cited by:

    1. Yue He & Reiichiro Kawai & Yasutaka Shimizu & Kazutoshi Yamazaki, 2022. "The Gerber-Shiu discounted penalty function: A review from practical perspectives," Papers 2203.10680, arXiv.org, revised Dec 2022.
    2. He, Yue & Kawai, Reiichiro & Shimizu, Yasutaka & Yamazaki, Kazutoshi, 2023. "The Gerber-Shiu discounted penalty function: A review from practical perspectives," Insurance: Mathematics and Economics, Elsevier, vol. 109(C), pages 1-28.
    3. Olena Ragulina & Jonas Šiaulys, 2020. "Upper Bounds and Explicit Formulas for the Ruin Probability in the Risk Model with Stochastic Premiums and a Multi-Layer Dividend Strategy," Mathematics, MDPI, vol. 8(11), pages 1-35, October.
    4. Georgios Psarrakos, 2015. "On the Integrated Tail of the Deficit in the Renewal Risk Model," Methodology and Computing in Applied Probability, Springer, vol. 17(2), pages 497-513, June.

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