The compound Poisson random variable’s approximation to the individual risk model

In this paper we study approximating the total loss associated with the individual insurance risk model by a compound Poisson random variable. By minimizing the expectation of the absolute deviation of the compound Poisson random variable from the true total loss, we investigate not only the optimal compound Poisson random variable but also the numerical calculation of the approximation error. We also discuss the influence of the Poisson parameter on the approximation error.