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Ruin Probabilities And Capital Requirement for Open Automobile Portfolios With a Bonus‐Malus System Based on Claim Counts

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  • Lourdes B. Afonso
  • Rui M. R. Cardoso
  • Alfredo D. Egídio dos Reis
  • Gracinda R. Guerreiro

Abstract

For a large motor insurance portfolio, on an open environment, we study the impact of experience rating in finite and continuous time ruin probabilities. We consider a model for calculating ruin probabilities applicable to large portfolios with a Markovian Bonus‐Malus System (BMS), based on claim counts, for an automobile portfolio using the classical risk framework model. New challenges are brought when an open portfolio scenario is introduced. When compared with a classical BMS approach ruin probabilities may change significantly. By using a BMS of a Portuguese insurer, we illustrate and discuss the impact of the proposed formulation on the initial surplus required to target a given ruin probability. Under an open portfolio setup, we show that we may have a significant impact on capital requirements when compared with the classical BMS, by having a significant reduction on the initial surplus needed to maintain a fixed level of the ruin probability.

Suggested Citation

  • Lourdes B. Afonso & Rui M. R. Cardoso & Alfredo D. Egídio dos Reis & Gracinda R. Guerreiro, 2020. "Ruin Probabilities And Capital Requirement for Open Automobile Portfolios With a Bonus‐Malus System Based on Claim Counts," Journal of Risk & Insurance, The American Risk and Insurance Association, vol. 87(2), pages 501-522, June.
    • Handle: RePEc:bla:jrinsu:v:87:y:2020:i:2:p:501-522
    DOI: 10.1111/jori.12300
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    References listed on IDEAS

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    1. Afonso, Lourdes B. & Cardoso, Rui M. R. & Egídio dos Reis, Alfredo D. & Guerreiro, Gracinda Rita, 2017. "Measuring The Impact Of A Bonus-Malus System In Finite And Continuous Time Ruin Probabilities For Large Portfolios In Motor Insurance," ASTIN Bulletin, Cambridge University Press, vol. 47(2), pages 417-435, May.
    2. 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.
    3. de Lourdes Centeno, Maria & Manuel Andrade e Silva, Joao, 2001. "Bonus systems in an open portfolio," Insurance: Mathematics and Economics, Elsevier, vol. 28(3), pages 341-350, June.
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    Cited by:

    1. 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.
    2. Osatakul, Dhiti & Li, Shuanming & Wu, Xueyuan, 2023. "Discrete-time risk models with surplus-dependent premium corrections," Applied Mathematics and Computation, Elsevier, vol. 437(C).
    3. Manuel L. Esquível & Nadezhda P. Krasii & Gracinda R. Guerreiro, 2021. "Open Markov Type Population Models: From Discrete to Continuous Time," Mathematics, MDPI, vol. 9(13), pages 1-29, June.
    4. M. Mercè Claramunt & Maite Mármol & Xavier Varea, 2023. "Facing a Risk: To Insure or Not to Insure—An Analysis with the Constant Relative Risk Aversion Utility Function," Mathematics, MDPI, vol. 11(5), pages 1-13, February.

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