On Error Bounds for Approximations to Aggregate Claims Distributions

In the present paper we discuss error bounds for approximations to aggregate claims distributions. We consider approximations to convolutions by approximitating each of the distributions and taking the convolution of these approximations. For compound distributions we consider two classes of approximations. In the first class we approximate the counting distribution, but keep the severity distribution unchanged, whereas in the second class we approximate the severity distribution, but keep the counting distribution unchanged. We finally look at some examples.