摘要翻译：
本文研究了亚式期权定价中退化抛物型偏微分方程初边值问题的可解性，并研究了这类方程解的微分性质和某些定性性质。利用有限差分格式得到的解，证明了边界退化模型的广义可解性。进一步研究了此类解的规律性。
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英文标题：
《Existence & Regularity of Weak Solutions of Degenerate Parabolic PDE
  Models for the Pricing of Security Derivatives》
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作者：
Rasoul Behboudi, You-Lan Zhu
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最新提交年份：
2009
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分类信息：

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：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：Numerical Analysis        数值分析
分类描述：Numerical algorithms for problems in analysis and algebra, scientific computation
分析和代数问题的数值算法，科学计算
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英文摘要：
  This work is focused on the solvability of initial-boundary value problems for degenerate parabolic partial differential equations that arise in the pricing of Asian options, and on the investigation of differential and certain qualitative properties of solutions of such equations. The generalized solvability for such models with degeneracy at the boundaries is proven by employing solutions obtained from finite difference numerical schemes. Furthermore, the regularity of such solutions is studied.
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PDF链接：
https://arxiv.org/pdf/0902.1721