Prediction of the reported but not settled (RBNS) claims reserves and the incurred but not reported (IBNR) claims reserves using the double chain ladder method

Abstract

An insurance company is required to set up a claims reserve to pay claims reported by the policyholders. There are two types of claims reserve: Reported but Not Settled (RBNS) claims reserve and Incurred but Not Reported (IBNR) claims reserve. Insurance company predicts a claims reserve using run-off triangle data. There are two types of data in a run-off triangle: claims amount and number of claims. The Chain Ladder (CL) Method is often used to estimate the claims reserve. In CL method, the claims reserve determined using the run-off triangle claims amount by calculated development pattern from the data and then calculated a predictive value of the claims reserve using that development pattern. But CL method unable to estimate the RBNS and IBNR reserves separately. The method used in this paper is closely related to CL method and is called a Double Chain Ladder (DCL) method. The DCL method applies the CL algorithm to two run-off triangles, the run-off triangle of claims amount and number of claims. The additional information from the run-off triangle of the number of claims enable the DCL method to estimate the RBNS and IBNR reserves separately. Based on numerical application, claims reserves obtained from CL and DCL methods are significantly different when there are many zero values in incremental run-off triangle.