Risk exchange II: Optimal reinsurance contracts

Abstract

Abstract The paper, a sequel to Taylor (1992), discusses risk exchange (REX) and reinsurance. A REX is global if its recoveries depend on just aggregate claims of the insurer in question; local if it depends on individual claims. A reinsurance is a 2-party REX under which recoveries are payable in only one direction between the two insurers; are dependent on the claims of only the insurer making the recoveries (the cedent); are non-negative; and do not exceed the direct claims on the cedent. Optimality of these forms of REX is discussed. In each case, the optimal REX is characterized (Sections 3 to 6). Optimization here consists of maximization of the expected terminal utility of the one of the two parties who acts as price taker, given the premium principle applied by the other party, who acts as price maker. Section 7 compares global and a particular class of local REXs in which individual recoveries are generated by individual claims and, perhaps surprisingly, find the former always preferable. Comment is made on reinsurance practice in the light of this result. Section 8 considers the shapes of the optimal reinsurance recovery functions identified in earlier sections, and compares these with the types of reinsurance encountered in practice. Key words: risk exchangeoptimal reinsuranceglobal reinsurancelocal reinsurance