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

Abstract

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.