英文标题：
《Change of measure up to a random time: Details》
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作者：
D\\\"orte Kreher
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最新提交年份：
2016
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英文摘要：
This paper extends results of Mortimer and Williams (1991) about changes of probability measure up to a random time under the assumptions that all martingales are continuous and that the random time avoids stopping times. We consider locally absolutely continuous measure changes up to a random time, changes of probability measure up to and after an honest time, and changes of probability measure up to a pseudo-stopping time. Moreover, we apply our results to construct a change of probability measure that is equivalent to the enlargement formula and to build for a certain class of pseudo-stopping times a class of measure changes that preserve the pseudo-stopping time property. Furthermore, we study for a price process modeled by a continuous semimartingale the stability of the No Free Lunch with Vanishing Risk (NFLVR) property up to a random time, that avoids stopping times, in the progressively enlarged filtration and provide sufficient conditions for this stability in terms of the Az\\\'ema supermartingale.
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中文摘要：
本文将Mortimer和Williams（1991）关于概率测度变化的结果推广到随机时间，假设所有鞅都是连续的，且随机时间避免停止时间。我们考虑了随机时间内的局部绝对连续测度变化，诚实时间内和诚实时间后的概率测度变化，以及伪停止时间内的概率测度变化。此外，我们应用我们的结果构造了一个等价于放大公式的概率测度变化，并为某类伪停止时间构造了一类保持伪停止时间性质的测度变化。此外，我们还研究了一个由连续半鞅建模的价格过程，在逐步扩大的过滤中，具有消失风险的非免费午餐（NFLVR）性质在随机时间内的稳定性，该性质避免了停止时间，并根据Az挈ema上鞅提供了这种稳定性的充分条件。
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分类信息：

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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一级分类：Quantitative Finance 数量金融学
二级分类：General Finance 一般财务
分类描述：Development of general quantitative methodologies with applications in finance
通用定量方法的发展及其在金融中的应用
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