英文标题：
《Convergence in Multiscale Financial Models with Non-Gaussian Stochastic
Volatility》
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作者：
Martino Bardi, Annalisa Cesaroni, Andrea Scotti
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最新提交年份：
2014
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英文摘要：
We consider stochastic control systems affected by a fast mean reverting volatility $Y(t)$ driven by a pure jump L\\\'evy process. Motivated by a large literature on financial models, we assume that $Y(t)$ evolves at a faster time scale $\\frac{t}{\\varepsilon}$ than the assets, and we study the asymptotics as $\\varepsilon\\to 0$. This is a singular perturbation problem that we study mostly by PDE methods within the theory of viscosity solutions.
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中文摘要：
我们考虑随机控制系统受快速均值回复波动率$Y（t）$的影响，该波动率由纯跳跃L趵evy过程驱动。受大量金融模型文献的启发，我们假设$Y（t）$的时间尺度$\\frac{t}{\\varepsilon}$比资产的时间尺度$\\frac{t}{\\varepsilon}$发展得更快，我们研究了$\\varepsilon\\到0$的渐近性。这是一个奇异摄动问题，我们主要用粘性解理论中的偏微分方程方法来研究。
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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：Mathematics 数学
二级分类：Analysis of PDEs 偏微分方程分析
分类描述：Existence and uniqueness, boundary conditions, linear and non-linear operators, stability, soliton theory, integrable PDE\'s, conservation laws, qualitative dynamics
存在唯一性，边界条件，线性和非线性算子，稳定性，孤子理论，可积偏微分方程，守恒律，定性动力学
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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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