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Bridging the gap between pricing and reserving with an occurrence and development model for non-life insurance claims

Author

Listed:
  • Jonas Crevecoeur
  • Katrien Antonio
  • Stijn Desmedt
  • Alexandre Masquelein

Abstract

Due to the presence of reporting and settlement delay, claim data sets collected by non-life insurance companies are typically incomplete, facing right censored claim count and claim severity observations. Current practice in non-life insurance pricing tackles these right censored data via a two-step procedure. First, best estimates are computed for the number of claims that occurred in past exposure periods and the ultimate claim severities, using the incomplete, historical claim data. Second, pricing actuaries build predictive models to estimate technical, pure premiums for new contracts by treating these best estimates as actual observed outcomes, hereby neglecting their inherent uncertainty. We propose an alternative approach that brings valuable insights for both non-life pricing as well as reserving. As such we effectively bridge these two key actuarial tasks that have traditionally been discussed in silos. Hereto we develop a granular occurrence and development model for non-life claims that tackles reserving and at the same time resolves the inconsistency in traditional pricing techniques between actual observations and imputed best estimates. We illustrate our proposed model on an insurance as well as a reinsurance portfolio. The advantages of our proposed strategy are most compelling in the reinsurance illustration where large uncertainties in the best estimates originate from long reporting and settlement delays, low claim frequencies and heavy (even extreme) claim sizes.

Suggested Citation

  • Jonas Crevecoeur & Katrien Antonio & Stijn Desmedt & Alexandre Masquelein, 2022. "Bridging the gap between pricing and reserving with an occurrence and development model for non-life insurance claims," Papers 2203.07145, arXiv.org, revised Feb 2023.
    • Handle: RePEc:arx:papers:2203.07145
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    References listed on IDEAS

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    1. Mack, Thomas, 1999. "The Standard Error of Chain Ladder Reserve Estimates: Recursive Calculation and Inclusion of a Tail Factor," ASTIN Bulletin, Cambridge University Press, vol. 29(2), pages 361-366, November.
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    7. Jewell, William S., 1990. "Predicting IBNYR Events and Delays II. Discrete Time," ASTIN Bulletin, Cambridge University Press, vol. 20(1), pages 93-111, April.
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    Cited by:

    1. Shengkun Xie & Rebecca Luo, 2022. "Measuring Variable Importance in Generalized Linear Models for Modeling Size of Loss Distributions," Mathematics, MDPI, vol. 10(10), pages 1-19, May.

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