Even convexity and optimization

MD Fajardo, MA Goberna, MML Rodrıguez… - Cham: Springer, 2020 - Springer
This is the first book devoted to linear systems of the form: σ={〈 at, x〉≤ bt, t∈ W;〈 at, x〉<
bt, t∈ S}, where〈·,·〉 denotes the standard inner product in Rn, W and S are arbitrary …

[HTML][HTML] Two fixed point theorems in complete random normed modules and their applications to backward stochastic equations

T Guo, E Zhang, Y Wang, Z Guo - Journal of Mathematical Analysis and …, 2020 - Elsevier
Abstract Let (Ω, F, F, P) be a filtered probability space with a filtration F=(F t) t∈[0, T]
satisfying the usual conditions and T a finite time, L 0 (F 0) the algebra of equivalence …

Conditional systemic risk measures

A Doldi, M Frittelli - SIAM Journal on Financial Mathematics, 2021 - SIAM
We investigate to which extent the relevant features of (static) Systemic Risk Measures can
be extended to a conditional setting. After providing a general dual representation result, we …

Complete duality for quasiconvex dynamic risk measures on modules of the Lp-type

M Frittelli, M Maggis - Statistics & Risk Modeling, 2014 - degruyter.com
In the conditional setting we provide a complete duality between quasiconvex risk measures
defined on L 0 modules of the L p type and the appropriate class of dual functions. This is …

Optimal Estimation Methodologies for Panel Data Regression Models

C Katsouris - arXiv preprint arXiv:2311.03471, 2023 - arxiv.org
This survey study discusses main aspects to optimal estimation methodologies for panel
data regression models. In particular, we present current methodological developments for …

On random convex analysis

T Guo, E Zhang, M Wu, B Yang, G Yuan… - arXiv preprint arXiv …, 2016 - arxiv.org
Recently, based on the idea of randomizing space theory, random convex analysis has
been being developed in order to deal with the corresponding problems in random …

L0-convex compactness and its applications to random convex optimization and random variational inequalities

T Guo, E Zhang, Y Wang, M Wu - Optimization, 2021 - Taylor & Francis
First, this paper introduces the notion of L 0-convex compactness for a special class of
closed convex subsets–closed L 0-convex subsets of a Hausdorff topological module over …

Real-valued systemic risk measures

A Doldi, M Frittelli - Mathematics, 2021 - mdpi.com
We describe the axiomatic approach to real-valued Systemic Risk Measures, which is a
natural counterpart to the nowadays classical univariate theory initiated by Artzner et al. in …

Evenly convex sets, and evenly quasiconvex functions, revisited

MA Goberna, M Rodríguez Álvarez, J Vicente-Perez - 2020 - rua.ua.es
Since its appearance, even convexity has become a remarkable notion in convex analysis.
In the fifties, W. Fenchel introduced the evenly convex sets as those sets solving linear …

Equilibrium, systemic risk measures and optimal transport: A convex duality approach

A Doldi - 2021 - air.unimi.it
This Thesis focuses on two main topics. Firstly, we introduce and analyze the novel concept
of Systemic Optimal Risk Transfer Equilibrium (SORTE), and we progressively generalize it …