Please use this identifier to cite or link to this item: https://hdl.handle.net/10419/324289 
Authors: 
Year of Publication: 
2024
Series/Report no.: 
Center for Mathematical Economics Working Papers No. 723
Publisher: 
Bielefeld University, Center for Mathematical Economics (IMW), Bielefeld
Abstract: 
The main result of this paper characterizes the continuity from below of monotone functionals on the space Cb of bounded continuous functions on an arbitrary Polish space as lower semicontinuity in the mixed topology. In this particular situation, the mixed topology coincides with the Mackey topology for the dual pair (Cb,ca), where ca denotes the space of all countably additive signed Borel measures of finite variation. Hence, lower semicontinuity in the mixed topology of convex monotone maps CbÇR is equivalent to a dual representation in terms of countably additive measures. Such representations are of fundamental importance in finance, e.g., in the context of risk measures and super hedging problems. Based on the main result, regularity properties of capacities and dual representations of Choquet integrals in terms of countably additive measures for 2-alternating capacities are studied. In a second step, the paper provides a characterization of equicontinuity in the mixed topology for families of convex monotone maps. As a consequence, for every convex monotone map on Cb taking values in a locally convex vector lattice, continuity in the mixed topology is equivalent to continuity on norm bounded sets.
Subjects: 
Risk measure
monotone functional
Choquet integral
continuity from below
lower semicontinuity
mixed topology
Mackey topology
Persistent Identifier of the first edition: 
Creative Commons License: 
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Document Type: 
Working Paper

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