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Mathematical Problems in Engineering
Volume 2016, Article ID 2371826, 6 pages
Research Article

Sparsity-Homotopy Perturbation Inversion Method with Wavelets and Applications to Black-Scholes Model and Todaro Model

1School of Finance, Harbin University of Commerce, Harbin 150028, China
2School of Management, Harbin University of Science and Technology, Harbin 150080, China

Received 17 April 2016; Accepted 28 June 2016

Academic Editor: Thomas Schuster

Copyright © 2016 Yixin Dou and Zhihao Wang. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.


Sparsity regularization method plays an important role in reconstructing parameters. Compared with traditional regularization methods, sparsity regularization method has the ability to obtain better performance for reconstructing sparse parameters. However, sparsity regularization method does not have the ability to reconstruct smooth parameters. For overcoming this difficulty, we combine a sparsity regularization method with a wavelet method in order to transform smooth parameters into sparse parameters. We use a sparsity-homotopy perturbation inversion method to improve the accuracy and stability and apply the proposed method to reconstruct parameters for a Black-Scholes option pricing model and a Todaro model. Numerical experiments show that the proposed method is convergent and stable.