On variational bounds in the compound Poisson approximation of the individual risk model

We present new upper bounds for the total variation distance between the aggregate claims distribution in the individual risk model and a suitable compound Poisson distribution. It turns out that the bounds are generally valid and contain so-called magic factors. Higher-order approximations, including the signed Kornya-Presman measures, are also investigated. In contrast to results of a previous paper by the author, the results do not depend on a joint decomposition of the individual claim amount distributions. Further, we do not need to assume the finiteness of moments.