A tempered subdiffusive Black-Scholes model

A computational weighted finite difference method for American and barrier options in subdiffusive Black-Scholes model

Subdiffusion is a well established phenomenon in physics. In this paper we apply the subdiffusive dynamics to analyze financial markets. We focus on the financial aspect of time fractional diffusion model with moving boundary i.e. American and barrier option pricing in the subdiffusive Black-Scholes (B-S) model. Two computational methods for valuing American options in the considered model are proposed - the weighted finite difference (FD) and the Longstaff-Schwartz method. In the article it is also shown how to valuate numerically wide range of barrier options using the FD approach.

通过可变指数推广次扩散Black-Scholes模型：模型变换与数值逼近

Generalizing subdiffusive Black-Scholes model by variable exponent: Model transformation and numerical approximation

本研究引入可变指数推广次扩散Black-Scholes模型以优化期权定价描述，通过时空变换解决可变指数记忆核难题，还完成数值格式分析与实验验证。

次扩散Black-Scholes模型的加权有限差分方法

A weighted finite difference method for subdiffusive Black Scholes Model

本文主要研究亚扩散的Black-Scholes模型。我们的工作的主要部分包括有限差分方法作为一种数值方法的期权定价所考虑的模型。我们推导了分数阶微分方程的控制方程和相应的加权数值格式，它是经典Crank-Nicolson格式的推广。所提出的方法具有$2-α$阶精度相对于时间，其中$α\in(0,1)$是子扩散参数，和$2$相对于空间。并给出了稳定性和收敛性分析。最后，我们给出了一些数值结果。

用于带缓增时间分数阶Black-Scholes模型的非等时间步快速紧致差分格式

A fast compact difference scheme with unequal time-steps for the tempered time-fractional Black-Scholes model

本研究针对带缓增时间分数阶Black-Scholes期权定价模型，结合非均匀时间步L1逼近与紧致差分构造格式，证明其无条件稳定，并用指数和逼近核函数实现快速计算以降低成本，数值实验验证了方法有效性。

使用径向基函数数值求解多维型 Black-Scholes 分数阶偏微分方程

Numerical solution using radial basis functions for multidimensional fractional partial differential equations of type Black-Scholes

本文提出使用基于径向基函数的无网格方法数值求解多维型 Black-Scholes 时间-空间分数阶偏微分方程，展示了该方法处理多维问题的灵活性及降低矩阵条件数的有效途径。