A Theory of Insurance Premiums

Abstract

The buyer of an insurance contract buys security, and the seller accepts a risk. The prem- ium charged by the seller must give him adequate compensation for the risk bearing service he provides, and of course be acceptable to the buyer. It is useful to see an insurance contract as a contingent claim. The buyer pays a premium in advance, and will get a random amount in return - as settlement of the claims he can make under the contract. Formally the transaction is of the same type as the purchase of a share in a risky business. The price of such shares is presumably determined by supply and demand in the market, and it is natural to assume that insurance premiums are determined in the same way. Economic theory has taken a long time to develop satisfactory models for the pricing of contingent claims. The breakthrough came just over thirty years ago, with the work of Arrow [1953]. In the following three decades a number of models have been developed, i.a. the so-called "Capital Asset Price Model" (CAPM) due to Sharpe [1964], Lintner [1965] and Mos- sin [1966], which has found extensive applications in practice.