Before revision:  In a second step, we consider dual representations of convex risk measures consistent with the premium principle. In particular, we show that the convex conjugate of the aforementioned maximal risk measure coincides with the convex conjugate of the premium principle on the set of all finitely additive probability measures. In a last step, we consider insurance prices in the presence of a not neccesarily frictionless market , where insurance claims are traded. In this setup, we discuss premium principles that are consistent with hedging using securization products that are traded in the market .
After revision:  In a second step, we consider dual representations of convex premium principles, and study the consistency of premium principles with a financial market in which insurance contracts are traded .