Comparison of Statistical Methods for Claims Reserve Estimation Using R Language

Abstract

Stochastic methods of reserves estimation serve to assess the technical provisions of outstanding claims and forecast cash payments of claims in the coming years. The chain ladder model developed by Mack is the more prevalent model. The main deficiency in the chain-ladder model is that the chain-ladder model depends on the last observation on the diagonal. If this last observation is an outlier, this outlier will be projected to the ultimate claim. One of the possibilities to smooth outliers on the last observed diagonal is to robustify such observations, making use of the maximum likelihood estimation along with the common Loss Development Factor (LDF) curve fitting and Cape Cod (CC) techniques. This paper aims to highlight the advantages of using these methods for the best estimate of claims reserves in the Domestic Motor Third Party Liability portfolio. The maximum–likelihood parameter estimation and Chi-square test, are used to specify the probability distribution that best fits the data. Using the Standard Chain Ladder method, LDF, and CC method the claims reserve is calculated based on the run-off triangles of paid claims or the run-off triangles of the incurred claims. Many times, the projections based on the paid claims are different than the projections based on the incurred claims. The solution for this problem is the Munich Chain Ladder method.