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Calculating Continuous Time Ruin Probabilities for a Large Portfolio with Varying Premiums

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

Abstract

In this paper we present a method for the numerical evaluation of the ruin probability in continuous and finite time for a classical risk process where the premium can change from year to year. A major consideration in the development of this methodology is that it should be easily applicable to large portfolios. Our method is based on the simulation of the annual aggregate claims and then on the calculation of the ruin probability for a given surplus at the start and at the end of each year. We calculate the within-year ruin probability assuming a translated gamma distribution approximation for aggregate claim amounts. We illustrate our method by studying the case where the premium at the start of each year is a function of the surplus level at that time or at an earlier time.

Suggested Citation

  • 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.
    • Handle: RePEc:cup:astinb:v:39:y:2009:i:01:p:117-136_00
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    Cited by:

    1. 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.
    2. 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.
    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. 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.
    5. 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.

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