摘要翻译：
在随机波动模型的一般框架下，我们分析了欧式未定权益的估值偏微分方程，其中扩散系数可能比线性增长更快，并在状态空间的边界上退化。我们考虑了各种类型的模型行为：我们的模型中的波动过程可能达到零，要么停留在那里，要么立即反映出来，资产-价格过程可能是一个严格的局部鞅。我们的主要结果是估值方程经典解唯一性的一个充要条件：当且仅当资产价格是鞅时，价值函数是估值方程在至多线性增长函数中唯一的非负经典解。
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英文标题：
《Valuation equations for stochastic volatility models》
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作者：
Erhan Bayraktar, Constantinos Kardaras, and Hao Xing
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最新提交年份：
2011
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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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英文摘要：
  We analyze the valuation partial differential equation for European contingent claims in a general framework of stochastic volatility models where the diffusion coefficients may grow faster than linearly and degenerate on the boundaries of the state space. We allow for various types of model behavior: the volatility process in our model can potentially reach zero and either stay there or instantaneously reflect, and the asset-price process may be a strict local martingale. Our main result is a necessary and sufficient condition on the uniqueness of classical solutions to the valuation equation: the value function is the unique nonnegative classical solution to the valuation equation among functions with at most linear growth if and only if the asset-price is a martingale.
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PDF链接：
https://arxiv.org/pdf/1004.3299