Estimation of outstanding claim reserves of motor vehicle third party insurance policies using chain ladder method

Abstract

This research aims at modeling outstanding claim reserves of motor vehicle third party insurance policies using inflation adjusted chain ladder and Basic / deterministic chain ladder method. The Chain Ladder (CL) Method is often used to estimate the claims reserve. In CL method, the claims reserve is 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. The dataset used for our analysis is from Kaggle datasets and ranges from 2013 to 2018. The analysis highlighted on estimating the total future outstanding liabilities, the outstanding claim liability for each development year, the development factors for each development period, determining the best method for the dataset and determining the growth pattern of the claims over the years. The run-off triangle assumptions used in previous studies were adopted i.e. 1. All claims are settled with a fixed number of development years 2. The incremental claim losses from the same number of accident years are well known until the present calendar year. 3. Development of losses of every accident year follows a development pattern which is common to all accident years. In this study, we found out that Basic/ deterministic chain ladder method had a better model fit for the dataset because of its small chi-square value (21260.54922) as compared to the inflation adjusted CL method (23493.59653). However, the reserve estimates for the inflation Adjusted Chain Ladder ($187,226.91) was smaller hence making it a more conservative method than the inflation unadjusted CL ($209,718). Further, report date and pay date had a statistically significant relationship with the indemnity amount paid. The cumulative claims had an increasing growth trend over the years of study. It is recommended that further research should be conducted to delve into more appropriate models that give best estimate and variability of claim reserves. The models developed here do not use any information from claim numbers and premium amounts. We recommend that if these were available, different actuarial models could be considered to take into account such parameters.