Core of the Reinsurance Market with Dependent Risks

Abstract

Baton and Lemaire (Astin Bull 12:57–71, 1981) proved the nonemptiness of the core of a reinsurance market in which the risks of companies are independent. However, cases involving dependent risks have received increasing concerns in modern actuarial science. In this paper, we investigate the nonemptiness of the core of a reinsurance market where the risks of different companies may be dependent. When the exponential utility function is employed, we find an important property on risk premium and show that the core of the market is always nonempty.