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The Gerber–Shiu discounted penalty function in a delayed renewal risk model with multi-layer dividend strategy

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  • Deng, Chao
  • Zhou, Jieming
  • Deng, Yingchun
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    Abstract

    A class of delayed renewal risk processes with multi-layer dividend strategy is addressed here. Under the assumption that the premium rate is a step function depending on the current surplus level, a piecewise integro-differential equation for the Gerber–Shiu discounted penalty function in the delayed renewal risk model is derived, as an analogue of that in the ordinary renewal model, and the relationship between this function and the one in the ordinary renewal model is investigated. Subsequently, this relationship is detailed as regards both the stationary renewal risk model and the ruin probability. Finally, explicit expressions for some ruin-related quantities are included to illustrate the procedure, where the inter-claim times are generalized Erlang(2) distributed and the claims are exponentially distributed.

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    Bibliographic Info

    Article provided by Elsevier in its journal Statistics & Probability Letters.

    Volume (Year): 82 (2012)
    Issue (Month): 9 ()
    Pages: 1648-1656

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    Handle: RePEc:eee:stapro:v:82:y:2012:i:9:p:1648-1656

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    Related research

    Keywords: Multi-layer dividend strategy; Delayed renewal risk process; Gerber–Shiu discounted penalty function; Ordinary renewal risk model; Time to ruin;

    References

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    1. Lin, X. Sheldon & Sendova, Kristina P., 2008. "The compound Poisson risk model with multiple thresholds," Insurance: Mathematics and Economics, Elsevier, vol. 42(2), pages 617-627, April.
    2. Lin, X.Sheldon & Pavlova, Kristina P., 2006. "The compound Poisson risk model with a threshold dividend strategy," Insurance: Mathematics and Economics, Elsevier, vol. 38(1), pages 57-80, February.
    3. Yang, Hu & Zhang, Zhimin, 2008. "Gerber-Shiu discounted penalty function in a Sparre Andersen model with multi-layer dividend strategy," Insurance: Mathematics and Economics, Elsevier, vol. 42(3), pages 984-991, June.
    4. Willmot, Gordon E., 2004. "A note on a class of delayed renewal risk processes," Insurance: Mathematics and Economics, Elsevier, vol. 34(2), pages 251-257, April.
    5. Willmot, Gordon E. & Dickson, David C. M., 2003. "The Gerber-Shiu discounted penalty function in the stationary renewal risk model," Insurance: Mathematics and Economics, Elsevier, vol. 32(3), pages 403-411, July.
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