Eberhard Mayerhofer

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We show that the only dynamic risk measure which is law invariant, time consistent and relevant is the entropic one. Moreover, a real valued function c on L ∞ (a, b) is normalized, strictly monotone, continuous, law invariant, time consistent and has the Fatou property if and only if it is of the form c(X) = u −1 • E [u(X)], where u : (a, b) → R is a(More)
We introduce a concept of causality in the framework of generalized pseudo-Riemannian Geometry in the sense of Colombeau. This is motivated by a generalized point value characterization of generalized pseudo-Riemannian metrics due to M. Kunzinger et al. We prove an appropriate version of the inverse Cauchy-Schwarz inequality. As an application, we establish(More)
We show that contrary to recent papers by S. Albeverio, A. Yu. Khrennikov and V. Shelkovich, point values do not determine elements of the so-called p-adic Colombeau-Egorov algebra G(Q n p) uniquely. We further show in a more general way that for an Egorov algebra G(M, R) of generalized functions on a locally compact ultrametric space (M, d) taking values(More)
We investigate homogeneity in the special Colombeau algebra on R d as well as on the pierced space R d \ {0}. It is shown that strongly scaling invariant functions on R d are simply the constants. On the pierced space, strongly homogeneous functions of degree α admit tempered representatives, whereas on the whole space, such functions are polynomials with(More)