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Ruin Probabilities with Dependence on the Number of Claims within a Fixed Time Window

Listed author(s):
  • Corina Constantinescu

    ()

    (Institute for Financial and Actuarial Mathematics, Department of Mathematical Sciences, University of Liverpool, Liverpool L69 7ZL, UK)

  • Suhang Dai

    ()

    (Institute for Financial and Actuarial Mathematics, Department of Mathematical Sciences, University of Liverpool, Liverpool L69 7ZL, UK)

  • Weihong Ni

    ()

    (Institute for Financial and Actuarial Mathematics, Department of Mathematical Sciences, University of Liverpool, Liverpool L69 7ZL, UK)

  • Zbigniew Palmowski

    ()

    (Mathematical Institute, University of Wrocław, Wroclaw 50-384, Poland)

Registered author(s):

    We analyse the ruin probabilities for a renewal insurance risk process with inter-arrival times depending on the claims that arrive within a fixed (past) time window. This dependence could be explained through a regenerative structure. The main inspiration of the model comes from the bonus-malus (BM) feature of pricing car insurance. We discuss first the asymptotic results of ruin probabilities for different regimes of claim distributions. For numerical results, we recognise an embedded Markov additive process, and via an appropriate change of measure, ruin probabilities could be computed to a closed-form formulae. Additionally, we employ the importance sampling simulations to derive ruin probabilities, which further permit an in-depth analysis of a few concrete cases.

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    Article provided by MDPI, Open Access Journal in its journal Risks.

    Volume (Year): 4 (2016)
    Issue (Month): 2 (June)
    Pages: 1-23

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    Handle: RePEc:gam:jrisks:v:4:y:2016:i:2:p:17-:d:72026
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    1. Albrecher, Hansjörg & Constantinescu, Corina & Loisel, Stephane, 2011. "Explicit ruin formulas for models with dependence among risks," Insurance: Mathematics and Economics, Elsevier, vol. 48(2), pages 265-270, March.
    2. Li, Bo & Ni, Weihong & Constantinescu, Corina, 2015. "Risk models with premiums adjusted to claims number," Insurance: Mathematics and Economics, Elsevier, vol. 65(C), pages 94-102.
    3. Afonso, Lourdes B. & dos Reis, Alfredo D. Egídio & Waters, Howard R., 2009. "Calculating Continuous Time Ruin Probabilities for a Large Portfolio with Varying Premiums," ASTIN Bulletin: The Journal of the International Actuarial Association, Cambridge University Press, vol. 39(01), pages 117-136, May.
    4. Albrecher, Hansjorg & Boxma, Onno J., 2004. "A ruin model with dependence between claim sizes and claim intervals," Insurance: Mathematics and Economics, Elsevier, vol. 35(2), pages 245-254, October.
    5. Søren Asmussen, 2014. "Modeling and Performance of Bonus-Malus Systems: Stationarity versus Age-Correction," Risks, MDPI, Open Access Journal, vol. 2(1), pages 1-25, March.
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