Modeling frequency distribution above a priority in presence of IBNR

TL;DR

This paper investigates modeling claim frequency above a priority level in reinsurance, demonstrating that both Poisson and Negative binomial models are consistent with Schnieper's framework, and introduces bootstrap methods for uncertainty quantification.

Contribution

It establishes the consistency of Schnieper's model with Poisson and Negative binomial distributions for claims above a priority, offering new modeling approaches and uncertainty management techniques.

Findings

Poisson model aligns with claims above priority in Schnieper's framework.

Negative binomial assumption yields similar modeling results.

Bootstrap procedure effectively manages parameter estimation uncertainty.

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 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.