Abstract
We consider the general problem sup мϵM ∫ƒdм|∫ƒdм=z 1(i=1…n) , where the integrals are over an abstract space Ω, the functions ƒ i (i =0)…..n ) are defined on that space, and where μm varies in a cone M of measures defined on the space. The integral on the left of the bar has to be maximized. The equalities on the right of the bar are further constraints on μ. The solution of this primal problem goes via the solution of an associated dual problem. The particular cases where M is the cone of positive measures and the cone of positive unimodal measures with fixed mode are investigated in more detail. Only two simple illustrations are given, but several actuarial applications are planned by De Vylder, Goovaerts and Haezendonck.
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