Approximating the finite-time ruin probability under interest force

We present an algorithm to determine both a lower and an upper bound for the finite-time probability of ruin for a risk process with constant interest force. We split the time horizon into smaller intervals of equal length and consider the probability of ruin in case premium income for a time interval 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 claim amount in a time interval. This distribution is determined through a generalization of Panjer’s [ASTIN Bulletin 12 (1981) 22] recursive method.