摘要翻译：
连续局部鞅$M$的随机指数$z_t=\exp\{M_t-M_0-(1/2)<m,m>_t\}$本身是连续局部鞅。在$m_t=\int_0^tb(Y_u)\，dw_u$和$y$为布朗运动驱动的一维扩散的情况下，给出了过程$z$为真鞅的充要条件。进一步，我们给出了$Z$是一致可积鞅的一个充要条件。这些条件是确定性的，仅用函数$B$和$Y$的漂移系数和扩散系数表示。作为一个应用，我们给出了一维环境中不存在气泡的确定性判据。
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英文标题：
《On the Martingale Property of Certain Local Martingales》
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作者：
Aleksandar Mijatovic, Mikhail Urusov
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最新提交年份：
2010
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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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英文摘要：
  The stochastic exponential $Z_t=\exp\{M_t-M_0-(1/2) <M,M>_t\}$ of a continuous local martingale $M$ is itself a continuous local martingale. We give a necessary and sufficient condition for the process $Z$ to be a true martingale in the case where $M_t=\int_0^t b(Y_u)\,dW_u$ and $Y$ is a one-dimensional diffusion driven by a Brownian motion $W$. Furthermore, we provide a necessary and sufficient condition for $Z$ to be a uniformly integrable martingale in the same setting. These conditions are deterministic and expressed only in terms of the function $b$ and the drift and diffusion coefficients of $Y$. As an application we provide a deterministic criterion for the absence of bubbles in a one-dimensional setting.
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PDF链接：
https://arxiv.org/pdf/0905.3701