The safest dependence structure among risks.

Abstract

In this paper, we investigate the dependence in Frechet spaces containing mutually exclusive risks. It is shown that, under some reasonable assumptions, the safest dependence structure, in the sense of the minimal stop-loss premiums for the aggregate claims involved, is obtained with the Frechet lower bound and precisely corresponds to the mutually exclusive risk of the Frechet space. In that respect, the present paper complements some previous studies by Heilmann (1986), Dhaene & Goovaerts (1996, 1997), Müller (1997) and Taizhong & Zhiqiang (1998). A couple of actuarial applications enhance the interest of the results derived.Dependence; Risk; Structure;