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02-02-2021 | Methodologies and Application

Optimal algebra and power series solution of fractional Black-Scholes pricing model

Authors: Hemanta Mandal, B. Bira, D. Zeidan

Published in: Soft Computing | Issue 8/2021

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Abstract

In the present article, we consider the time fractional Black-Scholes pricing model; governing in the fractal transmission system and describing the transaction costs in fractal market. From the application of symmetry analysis, we derive the infinitesimal transformations involving some arbitrary parameters; under which the equation remain invariant. Next, we write the set of operators corresponding to each of the parameter and under the full adjoint action, we construct and classify the finite dimensional optimal system of Lie algebras. Further, the similarity variables associated with one of the optimal algebra are used to reduce the governing fractional partial differential equations (FPDEs) to fractional ordinary differential equation (FODEs). Subsequently, we obtain the power series solution for the reduced FODEs which in turn produces the solution for the given FPDEs. Finally, we analyze its convergence and studied its behavior graphically under the influence of the fractional derivative.

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Title: Optimal algebra and power series solution of fractional Black-Scholes pricing model
Authors: Hemanta Mandal
B. Bira
D. Zeidan
Publication date: 02-02-2021
Publisher: Springer Berlin Heidelberg
Published in: Soft Computing / Issue 8/2021
Print ISSN: 1432-7643
Electronic ISSN: 1433-7479
DOI: https://doi.org/10.1007/s00500-021-05600-z

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