Approximating the finite-time ruin probability under interest force

We present an algorithm to determine both a lower and an upper bound for th e finite-time probability of ruin for a risk process with constant interest force. We split the time horizon into smaller intervals of equal length an d consider the probability of ruin in case premium income for a time interv al is received at the beginning (resp. end) of that interval, which yields a lower (resp. upper) bound. For both bounds we present a renewal equation which depends on the distribution of the present value of the aggregate cla im amount in a time interval. This distribution is determined through a gen eralization of Panjer's [ASTIN Bulletin 12 (1981) 22] recursive method. (C) 2001 Elsevier Science B.V. All tights reserved.