Randomized versions of Mazur lemma and Krein-\v{S}mulian Theorem with application to conditional convex risk measures for portfolio vectors
Randomized versions of Mazur lemma and Krein-\v{S}mulian Theorem with application to conditional convex risk measures for portfolio vectors
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发表时间：
2014-11
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通讯作者：
J. M. Zapata
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作者：
J. M. Zapata
引入局部L^0 $-凸模理论作为条件L^0 $-凸风险测度的分析基础.本文首先给出了这一理论的一些性质，并讨论了两类可数级联的性质。其次，我们推广了经典凸分析的一些结果，即我们提供了随机版本的Mazur引理和Krein-v {S}Mulian定理。第三，作为应用，我们建立了投资组合向量的条件凸风险度量的一个表示定理。
The theory of theory of locally $L^0$-convex modules was introduced as the analytic basis for conditional $L^0$-convex risk measures. In this paper we first give some preliminaries of this theory and discuss about two kinds of countable concatenation properties. Second we extend to this framework some results from classical convex analysis, namely we provide randomized versions of Mazur lemma and Krein-\v{S}mulian Theorem. Third, as application, we stablish a representation theorem for conditional convex risk measures for portfolio vectors.