Copula-based modeling for IBNR claim loss reserving

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 Chain-Ladder (CL) model forecasting.