Claim Reserving Using Tweedie Distribution

Abstract

Fitting mathematical regression models to insurance claims data has always been challenging. The problem is predominantly grave for data from individual policies where most of the losses are zero. In addition, those policies with an affirmative loss, the losses are highly skewed. Most of the traditional regression models do not deal with a mixture of discrete losses of zero and continuous positive losses. One way of dealing with this problem is to fit separate models to the frequency and severity. We address this problem using a new stochastic model called the Tweedie distribution model to derive estimates of outstanding Claims liabilities which are close to the chain ladder estimates. We take a broad view the gamma cell distributions model which leads to Tweedie's compound Poisson model. Choosing a suitable parameterization, we estimate the parameters of our model within the framework of generalized linear model. We show that these methods lead to rational estimates of the outstanding claims liabilities.