Novel ANN Method for Solving Ordinary and Time-Fractional Black–Scholes Equation

The main aim of this study is to introduce a 2-layered artificial neural network (ANN) for solving the Black–Scholes partial differential equation (PDE) of either fractional or ordinary orders. Firstly, a discretization method is employed to change the model into a sequence of ordinary differential...

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Bibliographic Details
Published in:Complexity (New York, N.Y.) N.Y.), 2021, Vol.2021 (1)
Main Authors: Bajalan, Saeed, Bajalan, Nastaran
Format: Article
Language:English
Subjects:
Artificial neural networks
Black-Scholes equation
Domains
Fractals
Interest rates
Investigations
Learning theory
Methods
Neural networks
Optimization
Ordinary differential equations
Partial differential equations
Securities markets
Securities prices
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Summary:The main aim of this study is to introduce a 2-layered artificial neural network (ANN) for solving the Black–Scholes partial differential equation (PDE) of either fractional or ordinary orders. Firstly, a discretization method is employed to change the model into a sequence of ordinary differential equations (ODE). Subsequently, each of these ODEs is solved with the aid of an ANN. Adam optimization is employed as the learning paradigm since it can add the foreknowledge of slowing down the process of optimization when getting close to the actual optimum solution. The model also takes advantage of fine-tuning for speeding up the process and domain mapping to confront the infinite domain issue. Finally, the accuracy, speed, and convergence of the method for solving several types of the Black–Scholes model are reported.
ISSN:1076-2787
1099-0526
DOI:10.1155/2021/5511396