论文标题
存在与亚洲选项相关的部分微分方程的基本解决方案
Existence of a Fundamental Solution of Partial Differential Equations associated to Asian Options
论文作者
论文摘要
我们证明了与某些随机过程相关的kolmogorov操作员的基本解决方案的存在和唯一性，这是在与依赖于路径相关的选项相关的Black＆Scholes设置中出现的。我们改善了以前的结果，因为我们在差异算子系数上的弱规则性假设下为凯奇问题的解决方案提供了封闭形式的表达。我们的方法基于一个限制程序，该程序的融合依赖于最近发现的一些障碍论点和统一的先验估计。
We prove the existence and uniqueness of the fundamental solution for Kolmogorov operators associated to some stochastic processes, that arise in the Black & Scholes setting for the pricing problem relevant to path dependent options. We improve previous results in that we provide a closed form expression for the solution of the Cauchy problem under weak regularity assumptions on the coefficients of the differential operator. Our method is based on a limiting procedure, whose convergence relies on some barrier arguments and uniform a priori estimates recently discovered.
