Calcul des Primes et Marchandage

Part I Two premium calculation principles by negotiation. Using, as main tools, the classical risk exchange model by Borch and the bargaining models of Nash and Kalai-Smorodinsky, we define two new premium calculation principles, whose main goal is to take explicitly into account the attitude towards risk of the policy-holders. Those principles are neither additive nor iterative, but they nevertheless possess several important properties: the premium is translation-invariant, it does not depend neither on the reserve nor on the portfolio of the company; it takes into account all the moments of the claim distribution; it is independent of the policy-holder's wealth but increases with his risk aversion. Part II Coalition against an insurance company. While computing the core of this risk exchange, we show that it can be of the policy-holder's interest to coalize in order to obtain premium cuts. * Article is in French