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Bonus-malus Systems vs Delays in Claims Reporting and Settlement: Analysis of Ruin Probabilities

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  • Dhiti Osatakul
  • Shuanming Li
  • Xueyuan Wu

Abstract

Our paper explores a discrete-time risk model with time-varying premiums, investigating two types of correlated claims: main claims and by-claims. Settlement of the by-claims can be delayed for one time period, representing real-world insurance practices. We examine two premium principles based on reported and settled claims, using recursively computable finite-time ruin probabilities to evaluate the performance of time-varying premiums. Our findings suggest that, under specific assumptions, a higher probability of by-claim settlement delays leads to lower ruin probabilities. Moreover, a stronger correlation between main claims and their associated by-claims results in higher ruin probabilities. Lastly, the premium adjustment principles based on settled claims experience contribute to higher ruin probabilities compared to those based on reported claims experience, assuming all other factors remain constant. Notably, this difference becomes more pronounced when there is a high likelihood of by-claim delays.

Suggested Citation

  • Dhiti Osatakul & Shuanming Li & Xueyuan Wu, 2024. "Bonus-malus Systems vs Delays in Claims Reporting and Settlement: Analysis of Ruin Probabilities," Papers 2408.00003, arXiv.org.
    • Handle: RePEc:arx:papers:2408.00003
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    References listed on IDEAS

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    1. Wagner, Christian, 2001. "A Note on Ruin in a Two State Markov Model1," ASTIN Bulletin, Cambridge University Press, vol. 31(2), pages 349-358, November.
    2. 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.
    3. Jie-hua Xie & Wei Zou, 2017. "Dividend barrier and ruin problems for a risk model with delayed claims," Communications in Statistics - Theory and Methods, Taylor & Francis Journals, vol. 46(14), pages 7063-7084, July.
    4. Afonso, Lourdes B. & Reis, Alfredo D. Egídio dos & Waters, Howard R., 2010. "Numerical Evaluation of Continuous Time Ruin Probabilities for a Portfolio with Credibility Updated Premiums," ASTIN Bulletin, Cambridge University Press, vol. 40(1), pages 399-414, May.
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