英文标题：
《On the martingale property in stochastic volatility models based on
  time-homogeneous diffusions》
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作者：
Carole Bernard, Zhenyu Cui, Don McLeish
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最新提交年份：
2014
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英文摘要：
  Lions and Musiela (2007) give sufficient conditions to verify when a stochastic exponential of a continuous local martingale is a martingale or a uniformly integrable martingale. Blei and Engelbert (2009) and Mijatovi\\\'c and Urusov (2012c) give necessary and sufficient conditions in the case of perfect correlation (\\rho=1). For financial applications, such as checking the martingale property of the stock price process in correlated stochastic volatility models, we extend their work to the arbitrary correlation case (-1<=\\rho<=1). We give a complete classification of the convergence properties of integral functionals of time-homogeneous diffusions and generalize results in Mijatovi\\\'c and Urusov (2012b) (2012c) with alternate proofs avoiding the use of separating times (concept introduced by Cherny and Urusov (2004) and extensively used in the proofs of Mijatovi\\\'c and Urusov (2012c)).
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中文摘要：
Lions和Musiela（2007）给出了证明连续局部鞅的随机指数是鞅还是一致可积鞅的充分条件。Blei和Engelbert（2009）以及Mijatoviêc和Urusov（2012c）给出了完全相关（\\rho=1）情况下的充分必要条件。对于金融应用，例如检查相关随机波动率模型中股票价格过程的鞅性质，我们将其工作扩展到任意相关情况（-1<=\\rho<=1）。我们给出了时间齐次扩散积分泛函的收敛性质的一个完整分类，推广了Mijatovi\'c和Urusov（2012b）（2012c）中的结果，并提供了避免使用分离时间的替代证明（Cherny和Urusov（2004）引入的概念，广泛用于Mijatovi\'c和Urusov（2012c）的证明）。
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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：Pricing of Securities        证券定价
分类描述：Valuation and hedging of financial securities, their derivatives, and structured products
金融证券及其衍生产品和结构化产品的估值和套期保值
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