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

Mathematical Modelling and Analysis

Ali Ebadian¹  Mohammadreza Foroutan²  Hadi Rahmani Fazli³ 

[1] Department of Mathematics, Faculty of Science, Urmia University Urmia, Iran;Department of Mathematics, Payame Noor University, P.O.Box 19395-3697, Tehran, Iran;Faculty of Economics, Allameh Tabataba’i University Tehran, Iran;

关键词: generalized Jacobi polynomials;    reproducing kernel Hilbert space method;    Black-Scholes equation;    Dirichlet boundary conditions;    error estimates;   

DOI  :  10.3846/mma.2018.032

来源: DOAJ

【 摘 要 】

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.

【 授权许可】

Unknown