Common Factor Risk Models Based on Negative Binomial Time series

Abstract

Insurance policies usually involve factors with greater risk of claims are charged at a higher rate. Therefore having efficient risk models is very important for insurers in estimating risk of insurance policies. Statistical methods and models for count data can be used to analyse or determine such insurance policy’s levels. In classical risk model, the claim numbers are usually determined by the underling risk of only one class. However, insurance businesses generally have more than one class of businesses. In recent year, many researchers are interested in studying risk models that the claim number is determined by exterior risk which affects more than one class. Therefore, the concept of common shock risk model is introduced. The common shock risk models originally assume the Poisson distribution. However, the property of having equal mean and variance of the Poisson distributions may not hold in some applications in particular when the data is over dispersed. Therefore, in this project, we construct common shock risk models based on negative binomial time series to study risk of any business where the claim numbers in the two classes of business may not be independent. In this study, we derive some probabilistic properties and the upper bound of the ruin probability. Moreover, numerical calculations of ruin probability in different cases are provided.