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英文标题：
《The Stochastic Solution to a Cauchy Problem for Degenerate Parabolic
Equations》
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作者：
Xiaoshan Chen, Yu-Jui Huang, Qingshuo Song, Chao Zhu
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最新提交年份：
2017
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英文摘要：
We study the stochastic solution to a Cauchy problem for a degenerate parabolic equation arising from option pricing. When the diffusion coefficient of the underlying price process is locally H\\\"older continuous with exponent $\\delta\\in (0, 1]$, the stochastic solution, which represents the price of a European option, is shown to be a classical solution to the Cauchy problem. This improves the standard requirement $\\delta\\ge 1/2$. Uniqueness results, including a Feynman-Kac formula and a comparison theorem, are established without assuming the usual linear growth condition on the diffusion coefficient. When the stochastic solution is not smooth, it is characterized as the limit of an approximating smooth stochastic solutions. In deriving the main results, we discover a new, probabilistic proof of Kotani\'s criterion for martingality of a one-dimensional diffusion in natural scale.
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中文摘要：
研究了由期权定价引起的退化抛物方程柯西问题的随机解。当基础价格过程的扩散系数为局部H \\“older连续，指数为$\\delta \\”（0，1]$，表示欧式期权价格的随机解是柯西问题的经典解。这改进了标准要求$\\delta\\ge 1/2$。在不假设扩散系数通常的线性增长条件的情况下，建立了唯一性结果，包括Feynman-Kac公式和比较定理on不是光滑的，它的特征是近似光滑随机解的极限。在推导主要结果的过程中，我们发现了一个新的概率证明，证明了自然尺度下一维扩散的Kotani鞅性判据。
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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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