英文标题：
《Obstacle problems for nonlocal operators》
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作者：
Donatella Danielli, Arshak Petrosyan, and Camelia A. Pop
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最新提交年份：
2017
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英文摘要：
  We prove existence, uniqueness, and regularity of viscosity solutions to the stationary and evolution obstacle problems defined by a class of nonlocal operators that are not stable-like and may have supercritical drift. We give sufficient conditions on the coefficients of the operator to obtain H\\\"older and Lipschitz continuous solutions. The class of nonlocal operators that we consider include non-Gaussian asset price models widely used in mathematical finance, such as Variance Gamma Processes and Regular L\\\'evy Processes of Exponential type. In this context, the viscosity solutions that we analyze coincide with the prices of perpetual and finite expiry American options.
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中文摘要：
我们证明了由一类非局部算子定义的平稳和演化障碍问题的粘性解的存在性、唯一性和正则性，这些算子不稳定，可能具有超临界漂移。我们给出了算子系数的充分条件，以获得H\\“older和Lipschitz连续解。我们考虑的非局部算子类包括在数学金融中广泛使用的非高斯资产价格模型，如方差Gamma过程和指数型正则L趵evy过程。在这种情况下，我们分析的粘性解与永久和有限到期美式期权的价格一致。
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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：Mathematical Finance        数学金融学
分类描述：Mathematical and analytical methods of finance, including stochastic, probabilistic and functional analysis, algebraic, geometric and other methods
金融的数学和分析方法，包括随机、概率和泛函分析、代数、几何和其他方法
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