29 citations · 65 across the 16 of their papers we have counts for
19 papers
On Prudence of Risk Measures
Niushan Gao, Denny H. Leung, Foivos Xanthos
Prudence is a stability property of risk functionals recently introduced by Wang and Zitikis and subsequently studied by Amarante and Liebrich. In this paper, we first establish ge…
On the sequential monotone closure of spaces
Sukrit Chalana, Denny H. Leung, Foivos Xanthos
In this short note, we settle a problem posed by Wickstead in ~\cite{W:24}, arising from the study of the Riesz completion of spaces of regular operators between Banach lattices.
A universal approximation theorem and its applications to vector lattice theory
Eugene Bilokopytov, Foivos Xanthos
A classical result in approximation theory states that for any continuous function \( φ: \mathbb{R} \to \mathbb{R} \), the set \( \operatorname{span}\{φ\circ g : g \in \operatornam…
Pervasiveness of in
Quinn Kiervin Starkey, Foivos Xanthos
Let be Archimedean Riesz spaces, and let denote an order completion of . In this note, we provide necessary conditions under which the space of regular operators $\…
A note on continuity and asymptotic consistency of measures of risk and variability
Niushan Gao, Foivos Xanthos
In this short note, we show that every convex, order bounded above functional on a Frechet lattice is automatically norm continuous. This improves a result in \cite{RS06} and appli…
On the extension property of dilatation monotone risk measures
Massoomeh Rahsepar, Foivos Xanthos
Let be a subset of that contains the space of simple random variables and a dilatation monotone func…
Stability properties of Haezendonck-Goovaerts premium principles
Niushan Gao, Cosimo Munari, Foivos Xanthos
We investigate a variety of stability properties of Haezendonck-Goovaerts premium principles on their natural domain, namely Orlicz spaces. We show that such principles always sati…
On local convexity in and switching probability measures
Niushan Gao, Denny H. Leung, Foivos Xanthos
In the paper, we investigate the following fundamental question. For a set in , when does there exist an equivalent probability measure $\ma…
A Local Hahn-Banach Theorem and Its Applications
Niushan Gao, Denny H. Leung, Foivos Xanthos
An important consequence of the Hahn-Banach Theorem says that on any locally convex Hausdorff topological space , there are sufficiently many continuous linear functionals to se…
The strong Fatou property of risk measures
Shengzhong Chen, Niushan Gao, Foivos Xanthos
In this paper, we explore several Fatou-type properties of risk measures. The paper continues to reveal that the strong Fatou property, which was introduced in [17], seems to be mo…
Duality for unbounded order convergence and applications
Niushan Gao, Denny H. Leung, Foivos Xanthos
Unbounded order convergence has lately been systematically studied as a generalization of almost everywhere convergence to the abstract setting of vector and Banach lattices. This…
Fatou Property, representations, and extensions of law-invariant risk measures on general Orlicz spaces
Niushan Gao, Denny H. Leung, Cosimo Munari +1
We provide a variety of results for (quasi)convex, law-invariant functionals defined on a general Orlicz space, which extend well-known results in the setting of bounded random var…
Closedness of convex sets in Orlicz spaces with applications to dual representation of risk measures
Niushan Gao, Denny H. Leung, Foivos Xanthos
Let be a conjugate pair of Orlicz functions. A set in the Orlicz space is said to be order closed if it is closed with respect to dominated convergence of sequences o…
Option spanning beyond -models
Niushan Gao, Foivos Xanthos
\begin{abstract} The aim of this paper is to study the spanning power of options in a static financial market that allows non-integrable assets. Our findings extend and unify the r…
On the C-property and -representations of risk measures
Niushan Gao, Foivos Xanthos
We identify a large class of Orlicz spaces for which the topology fails the C-property introduced in [7]. We also establish a variant of the C-property and use…
Uo-convergence and its applications to Cesàro means in Banach lattices
Niushan Gao, Vladimir G. Troitsky, Foivos Xanthos
A net in a vector lattice is said to uo-converge to if for every . In the first part of this paper, we study some func…
Spaces of regular abstract martingales
Vladimir G. Troitsky, Foivos Xanthos
In \cite{Troitsky:05,Korostenski:08}, the authors introduced and studied the space of regular martingales on a vector lattice and the space of bounded regular…
A version of Kalton's theorem for the space of regular operators
Foivos Xanthos
In this note we extend some recent results in the space of regular operators. In particular, we provide the following Banach lattice version of a classical result of Kalton: Let $E…
Unbounded Order Convergence and Application to Martingales without Probability
Niushan Gao, Foivos Xanthos
A net in a vector lattice is unbounded order convergent (uo-convergent) to if for each , and is unbounded o…