Stochastic Discounting, Aggregate Claims, and the Bootstrap

Obtaining good estimates for the distribution function of random variables like (.perpetuity.) and (.aggregate claim amount.), where the (Yi), (Zi) 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.