Reinsurance under Conditions of Capital Market Equilibrium: A Note*

HAVING ACCEPTED A CONTINGENT liability under an insurance contract, the insurer has an insurable interest in the subject of the insurance policy and can insure all or part of that liability with a second insurer. This reinsurance agreement protects the first insurer (known as the primary or ceding insurer) against unusually large claims, since it permits the risk to be broken down into smaller units which can be absorbed easily by individual insurers. These agreements are commonly placed with other direct insurers and with specialist reinsurance companies usually holding internationally diversified portfolios. The reinsurance agreement affects the risk return structure of the insurer's liability portfolio and consequently affects the risk-return characteristics of the insurer's common stock. The insurance literature has long assumed such reinsurance is an important procedure and much attention has been devoted to analyzing its use. Explicit statements of the objectives of reinsurance can be found in most insurance texts.' These texts commonly stress the portfolio risk effects of reinsurance, that is, the reduction in the probability of the failure (or "ruin") of the insurance fund and the stabilization of returns to its owners.2 The subdivision of policies and the spreading of risk between insurers permits each insurer to hold a more completely diversified portfolio of liabilities than would be available without reinsurance. Apart from explicit statements, the bulk of analytical literature on optimal reinsurance agreements has assumed risk reduction to be the objective. In earlier works, such as Vajda [15] and Ohlin [11], the benefits of reinsurance were identified in the reduction of the variance of the insurer's loss distribution. Subsequently, writers such as Borch [3, Chs. 1-11]; Buhlmann and Jewell [5]; Du Mouchel [6]; and Gerber [7] have used utility analysis to isolate the effects of reinsurance and to identify the properties of the optimal reinsurance treaty. Here, reinsurance is studied as a bilateral risk-reducing device arranged between two or more risk averse insurers. The Pareto condition has been evoked to define the optimality of a reinsurance treaty and, not surprisingly, it is shown to depend upon the form and parameters of the participating insurers' utility functions. The equilibrium conditions for reinsurance have also been established by Borch [3,