Lie symmetry analysis, and exact solutions to the time–fractional Black–Scholes equation of the Caputo–type

Najafi, Ramin; Bahrami, Fariba; Vafadar, Parisa

doi:10.22034/cmde.2024.59096.2510

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	Lie symmetry analysis, and exact solutions to the time–fractional Black–Scholes equation of the Caputo–type
Computational Methods for Differential Equations
مقاله 1، دوره 12، شماره 4، دی 2024، صفحه 638-650 اصل مقاله (625.84 K)
نوع مقاله: Research Paper
شناسه دیجیتال (DOI): 10.22034/cmde.2024.59096.2510
نویسندگان
Ramin Najafi^* ¹؛ Fariba Bahrami²؛ Parisa Vafadar²
¹Department of Mathematics, Maku Branch, Islamic Azad University, Maku, Iran.
²Faculty of Mathematics and Computer Science, University of Tabriz, Tabriz, Iran.
چکیده
In this study, the Lie symmetry analysis, and exact solutions are investigated to the fractional Black–Scholes(B-S) equations of the Caputo–type modeling of the pricing options under the absence of arbitrage and self-financing portfolio assumptions. A class of exact invariant and solitary solutions are given to B-S equations. Some examples are presented in which we use the obtained reductions to find their exact solutions.
کلیدواژه‌ها
Lie symmetry analysis؛ Time–fractional Black–Scholes equation؛ Caputo fractional derivative؛ Invariant solutions

مراجع
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Lie symmetry analysis, and exact solutions to the time–fractional Black–Scholes equation of the Caputo–type