Correlation Study between Individual Risk Models and Collective Risk Models for a Single Period

It is proved that the individual risk models for a single period are equivalent to the collective risk models for a single period when the number-of-claim random variable has 0-1 distribution. Furthermore, the individual risk model is close to a compound Poisson distribution when the number-of-claim random variable has a Poisson distribution with small parameter. Applying the Panjer iteration as calculation tool, the paper provides a novel solution to the problem for random variable calculating distribution of aggregate claims.