Modeling frequency distribution above a priority in presence of IBNR

Nicolas Baradel

Scandinavian Actuarial Journal, 2025, vol. 2025, issue 5, 532-547

Abstract: In reinsurance, Poisson and Negative binomial distributions are employed for modeling frequency. However, the incomplete data regarding reported incurred claims above a priority level presents challenges in estimation. This paper focuses on frequency estimation using Schnieper's framework [Schnieper, R. (1991). Separating true ibnr and ibner claims. ASTIN Bulletin, 21(1), 111–127.] for claim numbering. We demonstrate that Schnieper's model is consistent with a Poisson distribution for the total number of claims above a priority at each year of development, providing a robust basis for parameter estimation. Additionally, we explain how to build an alternative assumption based on a Negative binomial distribution, which yields similar results. The study includes a bootstrap procedure to manage uncertainty in parameter estimation and a case study comparing assumptions and evaluating the impact of the bootstrap approach.

Date: 2025
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DOI: 10.1080/03461238.2024.2439815

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