边界退化椭圆算子与Holder连续性 变分方程和不等式的解

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摘要翻译：
Heston随机波动过程是金融学中广泛应用的资产价格模型，它是一个退化扩散过程的范例，其中扩散系数的退化程度与到半平面边界距离的平方根成正比。该过程的生成元称为椭圆Heston算子，是一个二阶退化椭圆偏微分算子，其系数在空间变量中呈线性增长，算子符号中的退化度与到半平面边界的距离成正比。借助于加权Sobolev空间，我们证明了由椭圆Heston算子定义的变分方程解在边界附近的上确界、Harnack不等式和H“older连续性”，以及由椭圆Heston算子定义的变分不等式解在边界附近的H“older连续性”。在数学金融学中，椭圆Heston算子的障碍问题的解对应于标的资产的永久美式期权的价值函数。
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英文标题：
《Boundary-degenerate elliptic operators and Holder continuity for
  solutions to variational equations and inequalities》
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作者：
Paul M. N. Feehan and Camelia A. Pop
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最新提交年份：
2016
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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：Computational Finance        计算金融学
分类描述：Computational methods, including Monte Carlo, PDE, lattice and other numerical methods with applications to financial modeling
计算方法，包括蒙特卡罗，偏微分方程，格子和其他数值方法，并应用于金融建模
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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：
  The Heston stochastic volatility process, which is widely used as an asset price model in mathematical finance, is a paradigm for a degenerate diffusion process where the degeneracy in the diffusion coefficient is proportional to the square root of the distance to the boundary of the half-plane. The generator of this process with killing, called the elliptic Heston operator, is a second-order, degenerate-elliptic partial differential operator whose coefficients have linear growth in the spatial variables and where the degeneracy in the operator symbol is proportional to the distance to the boundary of the half-plane. With the aid of weighted Sobolev spaces, we prove supremum bounds, a Harnack inequality, and H\"older continuity near the boundary for solutions to variational equations defined by the elliptic Heston operator, as well as H\"older continuity up to the boundary for solutions to variational inequalities defined by the elliptic Heston operator. In mathematical finance, solutions to obstacle problems for the elliptic Heston operator correspond to value functions for perpetual American-style options on the underlying asset.
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PDF链接：
https://arxiv.org/pdf/1110.5594

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关键词：Holder Older hold 不等式 der 连续性 期权 equations 价值 距离