نظریه مخاطره با فرآیند گاما و کاربرد آن در بیمه شخص ثالث

In classical collective risk theory, the aggregate claims process is assumed to be a compound Poisson process with a finite number of claims in each time interval. Here we will examine a more general model for the aggregate claims process: Processes with independent, stationary and nonnegative increments. Such a process is a compound Poisson one or else a process with an infinite number of claims in any finite time interval. The most prominent process with this intriguing property is the gamma process. Since the compound Poisson process satisfies the above general assumptions, the properties of these processes can be derived from the basic properties of the compound Poisson process. It is shown how classical risk theory, and in particular ruin theory, can be adapted to this model. A detailed analysis is given for the gamma process, for which tabulated values of the probability of ruin and its bounds are provided. Finally, the model is applied to real data from third party car Insurance contracts obtained from Iranian Insurance Companies and the above mentioned characteristics of the model are calculated for this data