英文标题：
《On a Generalization of Markowitz Preference Relation》
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作者：
Valentin Vankov Iliev
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最新提交年份：
2016
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英文摘要：
Given two families of continuous functions $u$ and $v$ on a topological space $X$, we define a preorder $R=R(u,v)$ on $X$ by the condition that any member of $u$ is an $R$-increasing and any member of $v$ is an $R$-decreasing function. It turns out that if the topological space $X$ is quasi-compact and sequentially compact, then any element of $X$ is $R$-dominated by an $R$-maximal element of $X$. In particular, since the $(n-1)$-dimensional simplex is a compact subset of the real $n$-dimensional vector space, then considering its members as portfolios consisting of $n$ financial assets, we obtain the classical 1952 result of Harry Markowitz that any portfolio is dominated by an efficient portfolio. Moreover, several other examples of possible application of this general setup are presented.
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中文摘要：
给定拓扑空间$X$上的两个连续函数族$u$和$v$，我们定义了$X$上的一个前序$R=R（u，v）$，条件是$u$的任何成员是$R$增函数，$v$的任何成员是$R$减函数。结果表明，如果拓扑空间$X$是拟紧的且序列紧的，那么$X$的任何元素都是由$X$的$R$最大元素支配的$R$。特别是，由于$（n-1）$维单纯形是实$n$维向量空间的一个紧子集，然后将其成员视为由$n$金融资产组成的投资组合，我们得到了Harry Markowitz 1952年的经典结果，即任何投资组合都由有效投资组合支配。此外，还介绍了这种通用设置可能应用的几个其他示例。
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分类信息：

一级分类：Mathematics 数学
二级分类：Optimization and Control 优化与控制
分类描述：Operations research, linear programming, control theory, systems theory, optimal control, game theory
运筹学，线性规划，控制论，系统论，最优控制，博弈论
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一级分类：Quantitative Finance 数量金融学
二级分类：Portfolio Management 项目组合管理
分类描述：Security selection and optimization, capital allocation, investment strategies and performance measurement
证券选择与优化、资本配置、投资策略与绩效评价
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