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Exact Solution of Fractional Black-Scholes European Option Pricing Equations
Mathematics Department, Wuhan University of Technology, Wuhan, China
Mathematics Department, Wuhan University of Technology, Wuhan, China
- 1 Mathematics Department, Wuhan University of Technology, Wuhan, China
- 2 Mathematics Department, Wuhan University of Technology, Wuhan, China
Applied Mathematics·Volume 09 (2018)·Pages 86–100·Published 10 January 2018·DOI10.4236/am.2018.91006
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Abstract
We introduce two algorithms in order to find the exact solution of the nonlinear Time-fractional Partial differential equation, in this research work. Those algorithms are proposed in the following structure: The Modified Homotopy Perturbation Method (MHPM), The Homotopy Perturbation and Sumudu Transform Method. The results achieved using the both methods are the same. However, we calculate the approached theoretical solution of the Black-Scholes model in the form of a convergent power series with a regularly calculated element. Finally, we propose a descriptive example to demonstrate the efficiency and the simplicity of the methods.
KeywordsHomotopy Perturbation MethodModified Homotopy Perturbation MethodSumudu TransformBlack-Scholes Equations
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