Niveloids and their extensions: Risk measures on small domains

被引：18
作者：
Cerreia-Vioglio, S. [1 ,2 ]
Maccheroni, F. [1 ,2 ]
Marinacci, M. [1 ,2 ]
Rustichini, A. [1 ,2 ,3 ]
机构：
[1] Univ Bocconi, Milan, Italy
[2] IGIER, Naples, Italy
[3] Univ Minnesota, Minneapolis, MN 55455 USA
来源：
JOURNAL OF MATHEMATICAL ANALYSIS AND APPLICATIONS | 2014年 / 413卷 / 01期
关键词：
Extension theorems; Daniell-Stone Theorem; Risk measures; Variational preferences; AMBIGUITY;
D O I：
10.1016/j.jmaa.2013.11.034
中图分类号：
O29 [应用数学];
学科分类号：
070104 ;
摘要：
Given a functional defined on a nonempty subset of an Archimedean Riesz space with unit, necessary and sufficient conditions are obtained for the existence of a (convex or concave) niveloid that extends the functional to the entire space. In the language of mathematical finance, this problem is equivalent to the one of verifying if the policy adopted by a regulator is consistent with monetary risk measurement, when only partial information is available. (C) 2013 Elsevier Inc. All rights reserved.
引用
收藏
页码：343 / 360
页数：18
相关论文
共 23 条
  • [1] Aliprantis C., 2006, INFINITE DIMENSIONAL
  • [2] Aliprantis C. D., 2006, POSITIVE OPERATORS
  • [3] [Anonymous], ADV EC EC 10 WORLD C
  • [4] Coherent measures of risk
    Artzner, P
    Delbaen, F
    Eber, JM
    Heath, D
    [J]. MATHEMATICAL FINANCE, 1999, 9 (03) : 203 - 228
  • [5] Bhaskara Rao K.P.S., 1983, Theory of Charges
  • [6] Cerreia-Vioglio S., 2013, T AM MATH S IN PRESS
  • [7] Signed integral representations of comonotonic additive functionals
    Cerreia-Vioglio, Simone
    Maccheroni, Fabio
    Marinacci, Massimo
    Montrucchio, Luigi
    [J]. JOURNAL OF MATHEMATICAL ANALYSIS AND APPLICATIONS, 2012, 385 (02) : 895 - 912
  • [8] RISK MEASURES: RATIONALITY AND DIVERSIFICATION
    Cerreia-Vioglio, Simone
    Maccheroni, Fabio
    Marinacci, Massimo
    Montrucchio, Luigi
    [J]. MATHEMATICAL FINANCE, 2011, 21 (04) : 743 - 774
  • [9] Complete Monotone Quasiconcave Duality
    Cerreia-Vioglio, Simone
    Maccheroni, Fabio
    Marinacci, Massimo
    Montrucchio, Luigi
    [J]. MATHEMATICS OF OPERATIONS RESEARCH, 2011, 36 (02) : 321 - 339
  • [10] Choquet G., 1954, Ann. Institute. Fourier (Grenoble), V5, P131, DOI DOI 10.5802/AIF.53
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