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Uncertainty orders on the sublinear expectation space. (English) Zbl 1346.60013

Summary: In this paper, we introduce some definitions of uncertainty orders for random vectors in a sublinear expectation space. We all know that, under some continuity conditions, each sublinear expectation has a robust representation as the supremum of a family of probability measures. We describe uncertainty orders from two different viewpoints. One is from sublinear operator viewpoint. After giving definitions such as monotonic orders, convex orders and increasing convex orders, we use these uncertainty orders to derive characterizations for maximal distributions, \(G\)-normal distributions and \(G\)-distributions, which are the most important random vectors in the sublinear expectation space theory. On the other hand, we also establish some uncertainty orders’ characterizations from the viewpoint of probability measures and build some connections with the theory of risk measures.

MSC:

60E15 Inequalities; stochastic orderings
60H30 Applications of stochastic analysis (to PDEs, etc.)
91B06 Decision theory
90B50 Management decision making, including multiple objectives
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