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Generalized Jacobi reproducing kernel method in Hilbert spaces for solving the Black-Scholes option pricing problem arising in financial modelling

    Mohammadreza Foroutan Affiliation
    ; Ali Ebadian Affiliation
    ; Hadi Rahmani Fazli Affiliation

Abstract

Based on the reproducing kernel Hilbert space method, a new approach is proposed to approximate the solution of the Black-Scholes equation with Dirichlet boundary conditions and introduce the reproducing kernel properties in which the initial conditions of the problem are satisfied. Based on reproducing kernel theory, reproducing kernel functions with a polynomial form will be constructed in the reproducing kernel spaces spanned by the generalized Jacobi basis polynomials. Some new error estimates for application of the method are established. The convergence analysis is established theoretically. The proposed method is successfully used for solving an option pricing problem arising in financial modelling. The ideas and techniques presented in this paper will be useful for solving many other problems.

Keyword : generalized Jacobi polynomials, reproducing kernel Hilbert space method, Black-Scholes equation, Dirichlet boundary conditions, error estimates

How to Cite
Foroutan, M., Ebadian, A., & Fazli, H. (2018). Generalized Jacobi reproducing kernel method in Hilbert spaces for solving the Black-Scholes option pricing problem arising in financial modelling. Mathematical Modelling and Analysis, 23(4), 538-553. https://doi.org/10.3846/mma.2018.032
Published in Issue
Oct 9, 2018
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This work is licensed under a Creative Commons Attribution 4.0 International License.

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