英文标题：
《A system of non-local parabolic PDE and application to option pricing》
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作者：
Anindya Goswami, Jeeten Patel, Poorva Shevgaonkar
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最新提交年份：
2016
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英文摘要：
This paper includes a proof of well-posedness of an initial-boundary value problem involving a system of degenerate non-local parabolic PDE which naturally arises in the study of derivative pricing in a generalized market model. In a semi-Markov modulated GBM model the locally risk minimizing price function satisfies a special case of this problem. We study the well-posedness of the problem via a Volterra integral equation of second kind. A probabilistic approach, in particular the method of conditioning on stopping times is used for showing uniqueness.
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中文摘要：
本文证明了一类退化非局部抛物型偏微分方程组的初边值问题的适定性，这类问题在广义市场模型中的导数定价研究中自然出现。在半马尔可夫调制GBM模型中，局部风险最小化价格函数满足该问题的一个特例。我们通过第二类Volterra积分方程来研究问题的适定性。采用概率方法，尤其是停车时间条件化方法来显示唯一性。
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分类信息：

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：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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