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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].

MSC:

91B30 Risk theory, insurance (MSC2010)

Citations:

Zbl 1142.91045
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