Some Results on Optimal Reinsurance in Terms of the Adjustment Coefficient

Abstract A direct insurer wants to reinsure a certain part of a risk treaty. An underwriter who has been offered a reinsurance contract will rate the contract according to some premium principle. Depending on which premium principle the underwriter applies, the cedent will seek the type of reinsurance cover which gives him the best risk protection at a certain price. The paper is concerned with optimal reinsurance structures when the ceding insurer, and the reinsurer, seek to minimize the probability of eventual ruin. The cedent's, and reinsurer's, optimal choice of reinsurance is derived for various premium principles. Also the ‘Pareto optimal’ reinsurance structure is determined.