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摘要翻译：
本文背后的问题是交易的质量/可接受性/套利距离的恰当度量。通过增加一个数学性质，我们缩小了Cherny和Madan(2007)引入的相干可接受指数的范围。为此，我们引入凹畸变半群的概念，它是满足半群性质$$\psi_s\circ\psi_t=\psi_{s+t},\quad s,t\ge0的凹增函数$[0,1]\到[0,1]$的族$(\psi_t)_{t\ge0}$。本文的目的是从以下几个方面研究这些半群：失真半群的表示；从经济或数学角度考虑的畸变半群的性质；确定哪些凹畸变属于某些畸变半群。
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英文标题：
《Concave Distortion Semigroups》
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作者：
Alexander Cherny and Damir Filipovi\'c
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最新提交年份：
2011
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分类信息：
一级分类：Quantitative Finance 数量金融学
二级分类：Risk Management 风险管理
分类描述：Measurement and management of financial risks in trading, banking, insurance, corporate and other applications
衡量和管理贸易、银行、保险、企业和其他应用中的金融风险
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英文摘要：
The problem behind this paper is the proper measurement of the degree of quality/acceptability/distance to arbitrage of trades. We are narrowing the class of coherent acceptability indices introduced by Cherny and Madan (2007) by imposing an additional mathematical property. For this, we introduce the notion of a concave distortion semigroup as a family $(\Psi_t)_{t\ge0}$ of concave increasing functions $[0,1]\to[0,1]$ satisfying the semigroup property $$ \Psi_s\circ\Psi_t=\Psi_{s+t},\quad s,t\ge0. $$ The goal of the paper is the investigation of these semigroups with regard to the following aspects: representation of distortion semigroups; properties of distortion semigroups desirable from the economical or mathematical perspective; determining which concave distortions belong to some distortion semigroup.
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PDF链接：
https://arxiv.org/pdf/1104.0508
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