Abstract
In this study, we propose the concepts of sub-concave and sub-convex capacities. First, we investigate some properties of sub-concave and sub-convex capacities. Second, we discuss the Choquet integrals with respect to sub-concave and sub-convex capacities. We then show that the upper and lower probabilities comprising the supremum and infimum over the set of risk neutral martingale measures in the asymmetrical case are sub-concave and sub-convex capacities, respectively.
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