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Forecasting reserve risk for temporal dependent losses in insurance

Author

Listed:
  • Sawssen Araichi

    (LSAF - Laboratoire de Sciences Actuarielle et Financière - UCBL - Université Claude Bernard Lyon 1 - Université de Lyon)

  • Christian de Peretti

    (ECL - École Centrale de Lyon - Université de Lyon, LSAF - Laboratoire de Sciences Actuarielle et Financière - UCBL - Université Claude Bernard Lyon 1 - Université de Lyon)

  • Lotfi Belkacem

    (USO - جامعة سوسة = Université de Sousse = University of Sousse)

Abstract

In non‐life insurance, insurance companies aim to accurately assess their reserves in order to fulfil their future obligations. They are based on methods provided by the literature review to evaluate their reserve risk. However, these methods do not take all claim characteristics and ignore the temporal dependence structure of claims, which can affect reserve amounts and lead to delayed payments for policyholders. Therefore, the aim is to investigate the temporal dependence structure among claim amounts (losses) in order to evaluate the accurate amounts of reserves. To achieve this goal, a model called the Generalized Autoregressive Conditional Sinistrality Model is proposed, which considers the temporal dependence characteristics of claims. This model is used to estimate model parameters, so the consistency of such an estimate is proven. Additionally, a bootstrap method adjusted to the Generalized Autoregressive Conditional Sinistrality model is proposed for predicting reserves and errors. The results reveal that considering temporal dependence between losses improves reserve distribution estimation and enhances solvency capital requirement. This means that insurance companies will be able to ensure they have sufficient funds available to meet their obligations to policyholders, thereby enhancing customer satisfaction and trust. Additionally, this can assist insurance companies in maintaining better regulatory compliance.

Suggested Citation

  • Sawssen Araichi & Christian de Peretti & Lotfi Belkacem, 2024. "Forecasting reserve risk for temporal dependent losses in insurance," Post-Print hal-04875444, HAL.
    • Handle: RePEc:hal:journl:hal-04875444
    DOI: 10.1002/ijfe.3014
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    References listed on IDEAS

    as
    1. Swishchuk, Anatoliy & Zagst, Rudi & Zeller, Gabriela, 2021. "Hawkes processes in insurance: Risk model, application to empirical data and optimal investment," Insurance: Mathematics and Economics, Elsevier, vol. 101(PA), pages 107-124.
    2. Lee, Gee Y. & Shi, Peng, 2019. "A dependent frequency–severity approach to modeling longitudinal insurance claims," Insurance: Mathematics and Economics, Elsevier, vol. 87(C), pages 115-129.
    3. England, Peter & Verrall, Richard, 1999. "Analytic and bootstrap estimates of prediction errors in claims reserving," Insurance: Mathematics and Economics, Elsevier, vol. 25(3), pages 281-293, December.
    4. Md. Samsul Alam & Sajid Ali & Naceur Khraief & Syed Jawad Hussain Shahzad, 2021. "Time‐varying causal nexuses between economic growth and CO2 emissions in G‐7 countries: A bootstrap rolling window approach over 1820–2015," International Journal of Finance & Economics, John Wiley & Sons, Ltd., vol. 26(4), pages 6128-6148, October.
    5. Mack, Thomas, 1993. "Distribution-free Calculation of the Standard Error of Chain Ladder Reserve Estimates," ASTIN Bulletin, Cambridge University Press, vol. 23(2), pages 213-225, November.
    6. Antonio, Katrien & Beirlant, Jan, 2007. "Actuarial statistics with generalized linear mixed models," Insurance: Mathematics and Economics, Elsevier, vol. 40(1), pages 58-76, January.
    7. Araichi, Sawssen & Peretti, Christian de & Belkacem, Lotfi, 2016. "Solvency capital requirement for a temporal dependent losses in insurance," Economic Modelling, Elsevier, vol. 58(C), pages 588-598.
    8. Sawssen Araichi & Christian De Peretti & Lotfi Belkacem, 2016. "Solvency capital requirement for a temporal dependent losses in insurance," Post-Print hal-04875584, HAL.
    9. Davidson, Russell & MacKinnon, James G., 1993. "Estimation and Inference in Econometrics," OUP Catalogue, Oxford University Press, number 9780195060119.
    10. England, P.D. & Verrall, R.J., 2002. "Stochastic Claims Reserving in General Insurance," British Actuarial Journal, Cambridge University Press, vol. 8(3), pages 443-518, August.
    11. Shi, Peng & Feng, Xiaoping & Ivantsova, Anastasia, 2015. "Dependent frequency–severity modeling of insurance claims," Insurance: Mathematics and Economics, Elsevier, vol. 64(C), pages 417-428.
    12. Pešta, Michal & Okhrin, Ostap, 2014. "Conditional least squares and copulae in claims reserving for a single line of business," Insurance: Mathematics and Economics, Elsevier, vol. 56(C), pages 28-37.
    13. Avanzi, Benjamin & Taylor, Greg & Wong, Bernard, 2016. "Correlations Between Insurance Lines Of Business: An Illusion Or A Real Phenomenon? Some Methodological Considerations," ASTIN Bulletin, Cambridge University Press, vol. 46(2), pages 225-263, May.
    14. Michael Merz & Mario Wüthrich, 2008. "Prediction Error of the Multivariate Chain Ladder Reserving Method," North American Actuarial Journal, Taylor & Francis Journals, vol. 12(2), pages 175-197.
    15. Westerlund, Joakim & Narayan, Paresh, 2014. "Panel versus GARCH information in unit root testing with an application to financial markets," Economic Modelling, Elsevier, vol. 41(C), pages 173-176.
    16. Lu Yang & Peng Shi, 2019. "Multiperil rate making for property insurance using longitudinal data," Journal of the Royal Statistical Society Series A, Royal Statistical Society, vol. 182(2), pages 647-668, February.
    17. Paulo J. R. Pinheiro & João Manuel Andrade e Silva & Maria De Lourdes Centeno, 2003. "Bootstrap Methodology in Claim Reserving," Journal of Risk & Insurance, The American Risk and Insurance Association, vol. 70(4), pages 701-714, December.
    18. Bermúdez, Lluís & Karlis, Dimitris, 2011. "Bayesian multivariate Poisson models for insurance ratemaking," Insurance: Mathematics and Economics, Elsevier, vol. 48(2), pages 226-236, March.
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