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To address the plurality of interpretations of the subjective notion of risk, we describe it by means of a risk order and concentrate on the context invariant features of diversification and monotonicity. Our main results are uniquely characterized robust representations of lower semicontinuous risk orders on vector spaces and convex sets. This… (More)
In the paradigm of von Neumann and Morgenstern, a representation of ane preferences in terms of an expected utility can be obtained under the assumption of weak continuity. Since the weak topology is coarse, this requirement is a priori far from being negligible. In this work, we replace the assumption of weak continuity by monotonicity. More precisely, on… (More)
The classical Brouwer fixed point theorem states that in R d every continuous function from a convex, compact set on itself has a fixed point. For an arbitrary probability space, let L 0 = L 0 (, A, P) be the set of random variables. We consider (L 0) d as an L 0-module and show that local, sequentially continuous functions on L 0-convex, closed and bounded… (More)
We prove a closedness result for sets of lotteries that are monotone with respect to first order stochastic dominance and show how it can be applied to obtain robust representations of risk preferences on lotteries with compact support.