EconPapers    
Economics at your fingertips  
 

The Fatou property of law-invariant risk measures

Made Tantrawan and Denny H. Leung

Papers from arXiv.org

Abstract: This paper presents several results on the Fatou property of quasiconvex law-invariant functionals defined on a rearrangement invariant space $\mathcal{X}$. First, we show that for any proper quasiconvex law-invariant functional $\rho$ on $\mathcal{X}$, the Fatou property, $\sigma(\mathcal{X},\mathcal{X}_n^\sim)$-lower semicontinuity and $\sigma(\mathcal{X},L^\infty)$-lower semicontinuity of $\rho$ are equivalent, where $\mathcal{X}_n^\sim$ is the order continuous dual of $\mathcal{X}$. Second, we provide some relations between the Fatou property and some other types of lower semicontinuity, namely norm lower semicontinuity and the strong Fatou property. In particular, we show that when $\mathcal{X}\neq L^1$, the strong Fatou property and the Fatou property coincide. Finally, we generalize some extension results by Gao et al. [9] to a general rearrangement invariant space.

Date: 2018-10
References: View references in EconPapers View complete reference list from CitEc
Citations Track citations by RSS feed

Downloads: (external link)
http://arxiv.org/pdf/1810.10374 Latest version (application/pdf)

Related works:
This item may be available elsewhere in EconPapers: Search for items with the same title.

Export reference: BibTeX RIS (EndNote, ProCite, RefMan) HTML/Text

Persistent link: https://EconPapers.repec.org/RePEc:arx:papers:1810.10374

Access Statistics for this paper

More papers in Papers from arXiv.org
Bibliographic data for series maintained by arXiv administrators ().

 
Page updated 2018-11-24
Handle: RePEc:arx:papers:1810.10374