英文标题：
《A continuous selection for optimal portfolios under convex risk measures
  does not always exist》
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作者：
Michel Baes, Cosimo Munari
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最新提交年份：
2017
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英文摘要：
  One of the crucial problems in mathematical finance is to mitigate the risk of a financial position by setting up hedging positions of eligible financial securities. This leads to focusing on set-valued maps associating to any financial position the set of those eligible payoffs that reduce the risk of the position to a target acceptable level at the lowest possible cost. Among other properties of such maps, the ability to ensure lower semicontinuity and continuous selections is key from an operational perspective. It is known that lower semicontinuity generally fails in an infinite-dimensional setting. In this note we show that neither lower semicontinuity nor, more surprisingly, the existence of continuous selections can be a priori guaranteed even in a finite-dimensional setting. In particular, this failure is possible under arbitrage-free markets and convex risk measures.
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中文摘要：
数学金融学中的一个关键问题是通过建立合格金融证券的对冲头寸来降低金融头寸的风险。这就需要关注与任何财务状况相关的集值映射，即以尽可能低的成本将头寸风险降低到目标可接受水平的合格回报集。在这些映射的其他属性中，从操作角度来看，确保低半连续性和连续选择的能力是关键。众所周知，下半连续性通常在无限维环境中失效。在本文中，我们证明了即使在有限维环境中，也不能先验地保证下半连续性，更令人惊讶的是，连续选择的存在性。特别是，在无套利市场和凸风险度量下，这种失败是可能的。
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分类信息：

一级分类：Quantitative Finance        数量金融学
二级分类：Mathematical Finance        数学金融学
分类描述：Mathematical and analytical methods of finance, including stochastic, probabilistic and functional analysis, algebraic, geometric and other methods
金融的数学和分析方法，包括随机、概率和泛函分析、代数、几何和其他方法
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