ABSTRACT
Convex Function Classes . . . . . . . . . . . . . . . . . . . . . . . . . . . . 41 References . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 48
ABSTRACT
In this paper we review and extend some key results on the stochastic ordering of risks and on bounding the influence of stochastic dependence on risk functionals. The first part of the paper is concerned with a.s. constructions of random vectors and with diffusion kernel type comparisons which are of importance for various comparison results. In the second part
we consider generalizations of the classical Fre´chet-bounds, in particular for the distribution of sums and maxima and for more general monotonic functionals of the risk vector. In the final part we discuss three important orderings of risks which arise from -monotone, supermodular, and directionally convex functions. We give some new criteria for these orderings. For the basic results we also take care to give references to “original sources” of these results.
