Conditionally evenly convex sets and evenly quasi-convex maps

JOURNAL OF MATHEMATICAL ANALYSIS AND APPLICATIONS

卷:413

Article

Frittelli, Marco¹  Maggis, Marco¹ 

[1] Univ Milan, Dipartimento Matemat, I-20122 Milan, Italy

关键词: Evenly convex set;    Separation theorem;    Bipolar theorem;    L-0-modules;    Nonlinear conditional expectation;    Quasi-convex risk measures;   

DOI  :  10.1016/j.jmaa.2013.11.044

来源: Elsevier

【 摘 要 】

Evenly convex sets in a topological vector space are defined as the intersection of a family of open half spaces. We introduce a generalization of this concept in the conditional framework and provide a generalized version of the bipolar theorem. This notion is then applied to obtain the dual representation of conditionally evenly quasi-convex maps, which turns out to be a fundamental ingredient in the study of quasi-convex dynamic risk measures. (C) 2013 Elsevier Inc. All rights reserved.

【 授权许可】

Free