The Influence Of Outlying Claims On The Estimates Of Insurance Company’s Reserve

As an important item of debts, the estimate of claims reserve has been paid more attention by non-life insurance company to improve the competence. To forecast these claims reserves, the simple but generally accepted algorithm are the classical chain-ladder method.But when the payment data is insufficient, we can not get the accurate payment patterns, so people try to introduce some stochastic models to estimate the reserve, such as Generalized Linear Model (GLM) and Two-stage Generalized Linear Model. The introduction of the stochastic model greatly expands the non-life insurance reserving models.The outlying observation occurs frequently due to unexpected events, credit fraud or other problems, these data tend to prepare large deviation of the estimated results, and the finally influences operational decisions of the non-life insurance company. Therefore, this paper will study the impact of outlying observation to reserve estimates by comparing the commonly used models, and try to find a more reasonable model to provide a reference for insurance companies while forecasting these claims reserves.Based on the above discussion, the paper focuses on two another approaches:the Robust Chain-ladder method and Robust GLM. In addition, this paper propose Two-stage Robust GLM creatively based on Robust GLM and Two-stage GLM. Studies have shown that traditional reserving models are easily influenced by the outlying observation in the raw data, and robust generalized linear model is more robust when processing the data with outliers. For obtaining the corresponding standard errors the bootstrapping technique is applied. The robust method is applied to several run-off triangles with and without outliers, showing its excellent performance. Because the robust method flags the outliers, it is possible to examine these observations for further examination and insurance companies will be able to find a more accurate reserve.