Copula-based Modeling for IBNR Claim Loss Reserving

TL;DR

This paper introduces a copula-based dependency model to improve IBNR claim reserve estimation by capturing the relationship between occurrence and delay times, validated through simulation and real data application.

Contribution

It proposes a novel copula-based model for IBNR reserving and demonstrates its effectiveness compared to classical methods using real insurance data.

Findings

The copula model accurately captures dependencies between IBNR variables.

Simulation confirms the theoretical validity of the model.

Application shows improved forecasting over classical models.

Abstract

There are growing concerns for reserves estimation of incurred but not reported (IBNR) claims in actuarial sciences. In this paper, we propose a copula-based dependency model to capture the relationship between two main IBNR reserve variables, i.e., the time between two successive occurrences and delay time. A maximum likelihood estimation method is used to estimate the parameters of the model. A simulation study is conducted to evaluate the validity of the theoretical results. Moreover, the proposed method is applied to predict the number of claims for the next years of a portfolio from a major automobile insurer and is compared to the classical CL model forecasting.