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Generalized heat diffusion equations with variable coefficients and their fractalization from the Black-Scholes equation
Communications in Theoretical Physics ( IF 2.4 ) Pub Date : 2021-03-25 , DOI: 10.1088/1572-9494/abeb05 Rami Ahmad El-Nabulsi 1, 2, 3 , Alireza Khalili Golmankhaneh 4
中文翻译:
具有可变系数的广义热扩散方程及其来自 Black-Scholes 方程的分形
更新日期:2021-03-25
Communications in Theoretical Physics ( IF 2.4 ) Pub Date : 2021-03-25 , DOI: 10.1088/1572-9494/abeb05 Rami Ahmad El-Nabulsi 1, 2, 3 , Alireza Khalili Golmankhaneh 4
Affiliation
In this study, we prove that modified diffusion equations, including the generalized Burgers’ equation with variable coefficients, can be derived from the Black-Scholes equation with a time-dependent parameter based on the propagator method known in quantum and statistical physics. The extension for the case of a local fractal derivative is also addressed and analyzed.
中文翻译:
具有可变系数的广义热扩散方程及其来自 Black-Scholes 方程的分形
在这项研究中,我们证明了修正的扩散方程,包括具有可变系数的广义 Burgers 方程,可以从具有时间相关参数的 Black-Scholes 方程导出,该方程基于量子和统计物理学中已知的传播器方法。还讨论和分析了局部分形导数情况的扩展。