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

Author(s):

Ramin Najafi * , Fariba Bahrami , Parisa Vafadar

Message:
Article Type:
Research/Original Article (دارای رتبه معتبر)
Abstract:
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.
Keywords:

Lie Symmetry Analysis , Time–Fractional Black–Scholes Equation , Caputo Fractional Derivative , Invariant Solutions

Language:
English
Published:
Computational Methods for Differential Equations, Volume:12 Issue: 4, Autumn 2024
Pages:
638 to 650
https://magiran.com/p2762054