英文标题：
《Description of Incomplete Financial Markets for the Discrete Time
  Evolution of Risk Assets》
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作者：
N.S. Gonchar
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最新提交年份：
2018
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英文摘要：
  In the paper, the martingales and super-martingales relative to a regular set of measures are systematically studied. The notion of local regular super-martingale relative to a set of equivalent measures is introduced and the necessary and sufficient conditions of the local regularity of it in the discrete case are founded. The regular set of measures play fundamental role for the description of incomplete markets. In the partial case, the description of the regular set of measures is presented. The notion of completeness of the regular set of measures have the important significance for the simplification of the proof of the optional decomposition for super-martingales. Using this notion, the important inequalities for some random values are obtained. These inequalities give the simple proof of the optional decomposition of the majorized super-martingales. The description of all local regular super-martingales relative to the regular set of measures is presented. It is proved that every majorized super-martingale relative to the complete set of measures is a local regular one. In the case, as evolution of a risk asset is given by the discrete geometric Brownian motion, the financial market is incomplete and a new formula for the fair price of super-hedge is founded.
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中文摘要：
本文系统地研究了与正则测度集相关的鞅和超鞅。引入了局部正则超鞅相对于一组等价测度的概念，建立了离散情形下局部正则超鞅的充要条件。规则的衡量标准对于描述不完全市场起着基础性作用。在部分情况下，给出了正则测度集的描述。正则测度集的完备性概念对于简化超鞅的可选分解的证明具有重要意义。利用这个概念，得到了一些随机值的重要不等式。这些不等式给出了最优超鞅的可选分解的简单证明。给出了与正则测度集相关的所有局部正则超鞅的描述。证明了每一个相对于完备测度集的优化超鞅都是一个局部正则超鞅。在这种情况下，由于风险资产的演化是由离散几何布朗运动给出的，金融市场是不完全的，因此建立了一个新的超级套期公平价格公式。
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分类信息：

一级分类：Quantitative Finance        数量金融学
二级分类：Statistical Finance        统计金融
分类描述：Statistical, econometric and econophysics analyses with applications to financial markets and economic data
统计、计量经济学和经济物理学分析及其在金融市场和经济数据中的应用
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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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