Over Generalized Liner Model And Its Application In The Evaluation Of Outstanding Claims Reserve

Since the reform and opening up China’s economy has been growing rapidly, which also brings insurance industry into the fast lane. Insurance companies are confronted with fiercer competitions and more risks. Especially due to the uniqueness of insurance business, risks may occur when setting aside reserves. Outstanding claims reserve forms one of the major liabilities on non-life insurance company’s accounting statements. To guarantee solvency adequacy and profitability, it is essential to take into account the quantity and accuracy of reserves.Based on a series of quarterly data about paid loss and paid claim numbers from a listed insurance company from 2008 to 2013, and setting the development year and accident year age both from 1 to 24, this essay adopts discrete generalized linear model, Poisson distribution, generalized Poisson distribution, negative binomial distribution, and double Poisson distribution to fit paid claim numbers. Then cumulative losses of each claim is fitted with gamma distribution and inverse Gaussian distribution. After a comparative analysis, models with better fitness are selected respectively. Last, both models will run parameter estimation and prediction.Empirical evidences indicate that overdispersion appears in the data ofpaid claim numbers, thus leaving the results relatively less accurate when predicting with Poisson distribution. In perspective of the results in SAS, among the four distributions to model paid claim numbers, the values of AIC, AICC, and BIC from negative binominal distribution are the minimal. Hence the fitness to model paid claim numbers with negative binominal distribution is better than with other three distributions.