The Schmitter Problem

H. SCHMITTER describes the following practical background in which the problem arises. The problem of determining bounds for ruin probabilities arises when an insurer decides his reinsurance retentions m order to increase the stability of an account. He may not only choose between various forms of reinsurance (quota share, surplus, excess loss etc.) but he usually combines them in what is called a reinsurance program. When evaluating reinsurance programs he needs to compare their prices and the effectiveness of the protection they offer. The reinsurance price is the difference between the gross (i.e. before reinsurance) and the net 0.e. retained, after reinsurance) expected profit. The effectiveness of the protection, on the other hand, can be measured by the probability of ruin : the lower the probability of ruin of the retained account the more effective the reinsurance program. Computing ruin probabilities is often criticized as being pointless because their absolute values are said to be irrelevant. However, ff two reinsurance programs both reduce the expected profit of the ceding company by the same amount the one leading to the smaller probability of ruin is likely to be preferable.