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

Author

Listed:
  • 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)

Abstract

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.

Suggested Citation

  • Corina Constantinescu & Suhang Dai & Weihong Ni & Zbigniew Palmowski, 2016. "Ruin Probabilities with Dependence on the Number of Claims within a Fixed Time Window," Risks, MDPI, vol. 4(2), pages 1-23, June.
    • Handle: RePEc:gam:jrisks:v:4:y:2016:i:2:p:17-:d:72026
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    References listed on IDEAS

    as
    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. 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.
    4. Søren Asmussen, 2014. "Modeling and Performance of Bonus-Malus Systems: Stationarity versus Age-Correction," Risks, MDPI, vol. 2(1), pages 1-25, March.
    5. 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, Cambridge University Press, vol. 39(1), pages 117-136, May.
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    Cited by:

    1. Edita Kizinevič & Jonas Šiaulys, 2018. "The Exponential Estimate of the Ultimate Ruin Probability for the Non-Homogeneous Renewal Risk Model," Risks, MDPI, vol. 6(1), pages 1-17, March.
    2. Ka-Meng Siu & Ka-Hou Chan & Sio-Kei Im, 2023. "A Study of Assessment of Casinos’ Risk of Ruin in Casino Games with Poisson Distribution," Mathematics, MDPI, vol. 11(7), pages 1-15, April.
    3. Dhiti Osatakul & Xueyuan Wu, 2021. "Discrete-Time Risk Models with Claim Correlated Premiums in a Markovian Environment," Risks, MDPI, vol. 9(1), pages 1-23, January.
    4. Osatakul, Dhiti & Li, Shuanming & Wu, Xueyuan, 2023. "Discrete-time risk models with surplus-dependent premium corrections," Applied Mathematics and Computation, Elsevier, vol. 437(C).
    5. Wang, Zijia & Landriault, David & Li, Shu, 2021. "An insurance risk process with a generalized income process: A solvency analysis," Insurance: Mathematics and Economics, Elsevier, vol. 98(C), pages 133-146.

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