On the characterization of premium principle with respect to pointwise comonotonicity

A premium principle is an economic decision rule used by the insurer in order to determine the amount of the net premium for each risk in his portfolio. In this paper we investigate the problem how to determine the premium principle to be used. In Goovaerts & Dhaene (1997), DTEW Research Report 9740, K.U.Leuven, we can see some desirable properties of a premium principle. We consider a premium principle for risks of any sign, and prove a representation of premium principle without some property which involves the distribution of a risk. Later we introduce this property as a corollary