Exact calculations in the individual risk model are possible, but are very time consuming. Therefore, a number of recursive methods for approximate computation of the aggregate claims distribution and stop-loss premiums have been developed. In the present paper a general class of such approximation methods is considered, containing the higher order approximations suggested by Kornya, Hipp and De Pril. In this way, the treatment of the different methods is unified and extended to a more general setting. Some new theoretical error bounds are derived, giving a quantitative measure of the accuracy of the approximations.