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Some recent papers, as Zaks et al.(2006 ), Frostig et al.(2007 and Dhaene et al.(2009) , are dealing with capital allocation and premium pricing as optimization problems. In these papers the authors are considering some constraints on the convex function and they nd an explicit solution in each case. In this paper we prove the existence of a unique solution where each class has a dierent convex function. Moreover, we give an explicit solution in case the convex functions have a seconddoi:10.2139/ssrn.1625155 fatcat:3w223vqbprejrfcu7txvh6opgm