英文标题：
《Smallest order closed sublattices and option spanning》
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作者：
Niushan Gao, Denny H. Leung
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最新提交年份：
2017
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英文摘要：
Let $Y$ be a sublattice of a vector lattice $X$. We consider the problem of identifying the smallest order closed sublattice of $X$ containing $Y$. It is known that the analogy with topological closure fails. Let $\\overline{Y}^o$ be the order closure of $Y$ consisting of all order limits of nets of elements from $Y$. Then $\\overline{Y}^o$ need not be order closed. We show that in many cases the smallest order closed sublattice containing $Y$ is in fact the second order closure $\\overline{\\overline{Y}^o}^o$. Moreover, if $X$ is a $\\sigma$-order complete Banach lattice, then the condition that $\\overline{Y}^o$ is order closed for every sublattice $Y$ characterizes order continuity of the norm of $X$. The present paper provides a general approach to a fundamental result in financial economics concerning the spanning power of options written on a financial asset.
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中文摘要：
设$Y$是向量格$X$的子格。我们考虑了识别包含$Y$的$X$最小阶闭子格的问题。众所周知，拓扑闭包的类比是失败的。设$\\ overline{Y}^o$为$Y$的订单闭包，由$Y$中元素网络的所有订单限制组成。那么$\\第{Y}^行上的$^ o$就不需要关闭订单。我们表明，在许多情况下，包含$Y$的最小阶闭子格实际上是二阶闭包$\\ overline{\\ overline{Y}^o}^o$。此外，如果$X$是$\\ sigma$序完备Banach格，那么$\\ overline{Y}^o$对于每个子格$Y$是序闭的条件刻画了$X$范数的序连续性。本文提供了金融经济学关于金融资产期权跨越能力的基本结果的一般方法。
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分类信息：

一级分类：Mathematics 数学
二级分类：Functional Analysis 功能分析
分类描述：Banach spaces, function spaces, real functions, integral transforms, theory of distributions, measure theory
Banach空间，函数空间，实函数，积分变换，分布理论，测度理论
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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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