Obtaining good estimates for the distribution function of random variables like (‘perpetuity’) and (‘aggregate claim amount’), where the (Yi
) are independent i.i.d. sequences and (N(t)) is a general point process, is a key question in insurance mathematics. In this paper, we show how suitably chosen metrics provide a theoretical justification for bootstrap estimation in these cases. In the perpetuity case, we also give a detailed discussion of how the method works in practice.