This paper investigates the property of multivariance dependence among individual risks and studies its effect on the related stop-loss premiums. Among the aggregate claims, Hu-Wu (1999) found a type of negative dependency among individuals which gives rise to the safest aggregate claims, in the...

Using the perturbation in the 1/N,M as the exposure number, the leading correction to the claim number in the Longley-Cook theory is obtained. It is found that the correction term can not be neglected for common situations.