亚式期权偏微分方程基本解的存在性
Existence of a Fundamental Solution of Partial Differential Equations associated to Asian Options
摘要：
本文证明了在Black & Scholes环境下与路径相关期权定价问题有关的Kolmogorov算子的基本解的存在性和唯一性。我们改进了以前的结果，我们提供了一个封闭形式的表达式的柯西问题的解弱正则性假设下的系数的微分算子。我们的方法是基于一个限制过程，其收敛性依赖于一些障碍参数和统一的先验估计最近发现的。
英文摘要：
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.
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