Reinsurance and ruin

We study the effect of reinsurance on the probability of ultimate ruin in the classical surplus process and consider a retention level as optimal if it minimises the ruin probability. We show that optimal retention levels can be found when the reinsurer's premium loading depends on the retention level. We also show that when the aggregate claims process is approximated by a translated Gamma process, very good approximations to both optimal retention levels and ruin probabilities can be obtained. Finally, we discuss the effect of reinsurance on the probability of ruin in finite time.