Data di Pubblicazione:
2009
Citazione:
On the extension of the Namioka-Klee theorem and on the Fatou property for Risk Measures / S. Biagini, M. Frittelli - In: Optimality and risk : modern trends in mathematical finance : The Kabanov Festschrift / [a cura di] F. Delbaen, M. Rasonyi, Ch. Stricker. - Berlin : Springer, 2009. - ISBN 9783642026096. - pp. 1-28 [10.1007/978-3-642-02608-9_1]
Abstract:
This paper has been motivated by general considerations on the topic of Risk Measures, which essentially are convex monotone maps defined on spaces of random variables, possibly with the so-called Fatou property.
We show first that the celebrated Namioka-Klee theorem for linear, positive functionals holds also for convex monotone maps π on Frechet lattices.
It is well-known among the specialists that the Fatou property for risk measures on the space of bounded random variables enables a simplified dual representation, via probability measures only. The Fatou property in a general framework of lattices is nothing but the lower order semicontinuity property for π. Our second goal is thus to prove that a similar simplified dual representation holds also for order lower semicontinuous, convex and monotone functionals π defined on more general spaces (locally convex Frechet lattices). To this end, we identify a link between the topology and the order structure - the C-property - that enables the simplified representation. One main application of these results leads to the study of convex risk measures defined on Orlicz spaces and of their dual representation.
Tipologia IRIS:
03 - Contributo in volume
Keywords:
Convex monotone map; Locally convex Frechet lattice; Order (lower semi-)continuity; Fatou property; Dual representation
Elenco autori:
S. Biagini, M. Frittelli
Link alla scheda completa:
Titolo del libro:
Optimality and risk : modern trends in mathematical finance : The Kabanov Festschrift