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Numerical Evaluation of Continuous Time Ruin Probabilities for a Portfolio with Credibility Updated Premiums

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  • Afonso, Lourdes B.
  • Reis, Alfredo D. Egídio dos
  • Waters, Howard R.

Abstract

The probability of ruin in continuous and finite time is numerically evaluated in a classical risk process where the premium can be updated according to credibility models and therefore change from year to year. A major consideration in the development of this approach is that it should be easily applicable to large portfolios. Our method uses as a first tool the model developed by Afonso et al. (2009), which is quite flexible and allows premiums to change annually. We extend that model by introducing a credibility approach to experience rating. We consider a portfolio of risks which satisfy the assumptions of the Bühlmann (1967, 1969) or Bühlmann and Straub (1970) credibility models. We compute finite time ruin probabilities for different scenarios and compare with those when a fixed premium is considered.

Suggested Citation

  • 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.
    • Handle: RePEc:cup:astinb:v:40:y:2010:i:01:p:399-414_00
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    Cited by:

    1. Gauchon, Romain & Loisel, Stéphane & Rullière, Jean-Louis & Trufin, Julien, 2020. "Optimal prevention strategies in the classical risk model," Insurance: Mathematics and Economics, Elsevier, vol. 91(C), pages 202-208.
    2. Romain Gauchon & Stéphane Loisel & Jean-Louis Rullière & Julien Trufin, 2019. "Optimal prevention strategies in the classical risk model," Working Papers hal-02314899, HAL.
    3. Osatakul, Dhiti & Li, Shuanming & Wu, Xueyuan, 2023. "Discrete-time risk models with surplus-dependent premium corrections," Applied Mathematics and Computation, Elsevier, vol. 437(C).
    4. 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.
    5. Landriault, David & Lemieux, Christiane & Willmot, Gordon E., 2012. "An adaptive premium policy with a Bayesian motivation in the classical risk model," Insurance: Mathematics and Economics, Elsevier, vol. 51(2), pages 370-378.
    6. Li, Shu & Landriault, David & Lemieux, Christiane, 2015. "A risk model with varying premiums: Its risk management implications," Insurance: Mathematics and Economics, Elsevier, vol. 60(C), pages 38-46.

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