Spatial Joint Modeling of Claim Frequency and Claim Size in Third-Party Car Insurance of Iran Based on Copula Functions

The number of claims and the amount of claims (or the sum of claims, which is referred to as the amount of total claims/loss in the insurance literature) is among the most important information available to insurance companies, and its analysis can provide the necessary knowledge for targeted planning. In this paper, a spatial approach is studied for joint modeling of claim frequency and claim size. It is assumed that the number of accidents follows a Poisson distribution with a variable mean, and this mean in turn has a distribution that is usually referred to as a mixed distribution. Then, the spatial dependence structure within the observations is modeled using an appropriate copula function. Considering a similar framework for the conditional distribution of total claim size given the number of claims, the corresponding data will also be modeled. Finally, by estimating the parameters of the proposed model, the predictionmap for both claim frequencies and totatl claim size will be drawn and the cities or provinces of Iran with the highest number of claims and the highest amount of claims will be predicted