摘要翻译：
半静态套期保值在金融市场中的重要应用自然导致了准自对偶过程的概念。我们研究的重点是给出指数L\'Evy过程的拟自对偶的新刻画，使得所得到的市场不允许套利机会。本文给出了拟自对偶鞅模型随机对数的一组等价条件，并在不依赖于L\'Evy-Khintchine参数化的情况下给出了这些模型的进一步刻画。由于对于非消失序参量，必须同时满足两个鞅性质，因此在金融应用中表示携带成本的序参量与移位参量之间存在非平凡关系。这就导致了一个包含积分项的方程，该方程在应用中必须被反演。我们首先讨论了该方程的几个重要性质，并对一些已知的模型，导出了一族闭式反演公式，在已知的L\'Evy驱动模型的相应参数空间中，导出了可能组合集的参数化。
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英文标题：
《Quasi self-dual exponential L\'evy processes》
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作者：
Thorsten Rheinl\"ander and Michael Schmutz
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最新提交年份：
2012
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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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一级分类：Mathematics        数学
二级分类：Probability        概率
分类描述：Theory and applications of probability and stochastic processes: e.g. central limit theorems, large deviations, stochastic differential equations, models from statistical mechanics, queuing theory
概率论与随机过程的理论与应用：例如中心极限定理，大偏差，随机微分方程，统计力学模型，排队论
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英文摘要：
  The important application of semi-static hedging in financial markets naturally leads to the notion of quasi self-dual processes. The focus of our study is to give new characterizations of quasi self-duality for exponential L\'evy processes such that the resulting market does not admit arbitrage opportunities. We derive a set of equivalent conditions for the stochastic logarithm of quasi self-dual martingale models and derive a further characterization of these models not depending on the L\'evy-Khintchine parametrization. Since for non-vanishing order parameter two martingale properties have to be satisfied simultaneously, there is a non-trivial relation between the order and shift parameter representing carrying costs in financial applications. This leads to an equation containing an integral term which has to be inverted in applications. We first discuss several important properties of this equation and, for some well-known models, we derive a family of closed-form inversion formulae leading to parameterizations of sets of possible combinations in the corresponding parameter spaces of well-known L\'evy driven models.
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PDF链接：
https://arxiv.org/pdf/1201.5132