A novel numerical scheme for a time fractional Black-Scholes equation

被引：15
|
作者：
She, Mianfu [1 ,2 ]
Li, Lili [1 ]
Tang, Renxuan [1 ]
Li, Dongfang [1 ,2 ]
机构：
[1] Huazhong Univ Sci & Technol, Sch Math & Stat, Wuhan 430074, Peoples R China
[2] Huazhong Univ Sci & Technol, Hubei Key Lab Engn Modeling & Sci Comp, Wuhan 430074, Peoples R China
来源：
JOURNAL OF APPLIED MATHEMATICS AND COMPUTING | 2021年 / 66卷 / 1-2期
基金：
中国国家自然科学基金;
关键词：
Time-fractional Black– Scholes model; Chebyshev-Galerkin spectral method; Change of variable; Modified L1 scheme; DOUBLE-BARRIER OPTIONS; DIFFERENCE SCHEME; SPECTRAL METHOD; APPROXIMATION; MODEL;
D O I：
10.1007/s12190-020-01467-9
中图分类号：
O29 [应用数学];
学科分类号：
070104 ;
摘要：
This paper consists of two parts. On one hand, the regularity of the solution of the time-fractional Black-Scholes equation is investigated. On the other hand, to overcome the difficulty of initial layer, a modified L1 time discretization is presented based on a change of variable. And the spatial discretization is done by using the Chebyshev Galerkin method. Optimal error estimates of the fully-discrete scheme are obtained. Finally, several numerical results are given to confirm the theoretical results.
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页码：853 / 870
页数：18
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