Biagini, Sara; Frittelli, Marco On the extension of the Namioka-Klee theorem and on the Fatou property for risk measures. (English) Zbl 1188.91085 Delbaen, Freddy (ed.) et al., Optimality and risk – modern trends in mathematical finance. The Kabanov Festschrift. Berlin: Springer (ISBN 978-3-642-02607-2/hbk). 1-28 (2009). The authors prove that the celebrated Namioka-Klee theorem also holds for convex monotone maps on Fréchet lattices, and apply their findings to the dual representation of order lower semicontinuous convex monotone functionals defined on locally convex Fréchet lattices. The order structure plays the main part, as developed in the reviewer’s paper [G. Stoica, J. Math. Econ. 42, No. 6, 794–806 (2006; Zbl 1142.91045)].For the entire collection see [Zbl 1179.91005]. Reviewer: George Stoica (Saint John) Cited in 1 ReviewCited in 45 Documents MSC: 91B30 Risk theory, insurance (MSC2010) Keywords:convex monotone map; locally convex Frèchet lattice; order (lower semi-)continuity; Fatou property; dual representation Citations:Zbl 1142.91045 PDFBibTeX XMLCite \textit{S. Biagini} and \textit{M. Frittelli}, in: Optimality and risk -- modern trends in mathematical finance. The Kabanov Festschrift. Berlin: Springer. 1--28 (2009; Zbl 1188.91085)