STOCHASTIC DISCOUNTING, AGGREGATE CLAIMS, AND THE BOOTSTRAP

Obtaining good estimates for the distribution function of random varia bles like S = SIGMA(i=1)infinity Z1 ... Z(i)Y(i) ('perpetuity') and S( N(t)) = SIGMA(i=1)N(t) Y(i) ('aggregate claim amount'), where the (Y(i )), (Z(i)) are independent i.i.d. sequences and (N(t)) is a general po int process, is a key question in insurance mathematics. In this paper , we show how suitably chosen metrics provide a theoretical justificat ion for bootstrap estimation in these cases. In the perpetuity case, w e also give a detailed discussion of how the method works in practice.