Numerical Technique for the Solution ofFractional-Order Black-Scholes DifferentialEquation Using Neural Network Method
DOI:
https://doi.org/10.26713/cma.v17i1.3600Keywords:
Fractional Partial Differential Equation, Neural Networks, Fractional Black-Scholes, \(L^2\)-error, Shifted LegendreAbstract
The proposed paper presents a novel result for the fractional-order Black-Scholes differential equation (FOBSDE) using the neural network method (NNM). The proposed approach is constructed using utilizes spectral approximation and shifted Legendre polynomials and neural network optimization. The accuracy and efficiency of the method are demonstrated by numerous numerical experiments, and demonstrate that the method is superior to conventional numerical methods. Such results indicate what neural networks are able to do in solving complex fractional partial differential equations, which is a strong foundation of financial modeling.
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