Approximation Of Short-term Individual Risk Model Based On Compound Negative Binomial Variable

This paper mainly studies the approximation of total claims in the short-term individual risk model.Firstly,the claim times in the short-term individual risk model is assumed as negative binomial random variable,and a compound negative binomial model is established.The approximation is more accurate by minimizing the expectation of the absolute deviation between the compound negative binomial random variable and the actual total loss.Secondly,some general distribution properties are given,such as mean,variance and joint distribution of the model.Then we discusses the negative binomial parameter on the influence of approximation error and the error to minimize negative binomial parameter determination method,and the homogeneous short-term individual risk models are simulated,it also discusses the total losses and correlation function approximation.The compound negative binomial approximation of different short-term individual risk models is also given in this paper.