Fatou property,representations, and extensions of law-invariant risk measures on general Orlicz spaces |
| |
Authors: | Email author" target="_blank">Niushan?GaoEmail author Denny?Leung Cosimo?Munari Foivos?Xanthos |
| |
Institution: | 1.Department of Mathematics and Computer Science,University of Lethbridge,Lethbridge,Canada;2.Department of Mathematics,National University of Singapore,Singapore,Singapore;3.Center for Finance and Insurance,University of Zurich,Zurich,Switzerland;4.Department of Mathematics,Ryerson University,Toronto,Canada |
| |
Abstract: | We provide a variety of results for quasiconvex, law-invariant functionals defined on a general Orlicz space, which extend well-known results from the setting of bounded random variables. First, we show that Delbaen’s representation of convex functionals with the Fatou property, which fails in a general Orlicz space, can always be achieved under the assumption of law-invariance. Second, we identify the class of Orlicz spaces where the characterization of the Fatou property in terms of norm-lower semicontinuity by Jouini, Schachermayer and Touzi continues to hold. Third, we extend Kusuoka’s representation to a general Orlicz space. Finally, we prove a version of the extension result by Filipovi? and Svindland by replacing norm-lower semicontinuity with the (generally non-equivalent) Fatou property. Our results have natural applications to the theory of risk measures. |
| |
Keywords: | |
本文献已被 SpringerLink 等数据库收录! |
|