Efficient Scheme for the Economic Heston–Hull–White Problem Using Novel RBF-FD Coefficients Derived from Multiquadric Function Integrals-Reference-Cited by-同舟云学术

Efficient Scheme for the Economic Heston–Hull–White Problem Using Novel RBF-FD Coefficients Derived from Multiquadric Function Integrals

Published:2024-07-17 Issue:14 Volume:12 Page:2234
ISSN:2227-7390
Container-title:Mathematics
language:en
Short-container-title:Mathematics

Author:

Liu Tao¹^ORCID,Zhao Zixiao¹,Ling Shiyi¹,Chao Heyang¹,Nafchi Hasan Fattahi²,Shateyi Stanford³^ORCID

Affiliation:

1. School of Mathematics and Statistics, Northeastern University at Qinhuangdao, Qinhuangdao 066004, China

2. Department of Accounting, Faculty of Administrative Sciences and Economics, University of Isfahan, Isfahan 81746-73441, Iran

3. Department of Mathematics and Applied Mathematics, School of Mathematical and Natural Sciences, University of Venda, P. Bag X5050, Thohoyandou 0950, South Africa

Abstract

This study presents an efficient method using the local radial basis function finite difference scheme (RBF-FD). The innovative coefficients are derived from the integrals of the multiquadric (MQ) function. Theoretical convergence rates for the coefficients used in function derivative approximation are provided. The proposed scheme utilizes RBF-FD estimations on three-point non-uniform stencils to construct the final approximation on a tensor grid for the 3D Heston–Hull–White (HHW) PDE, which is relevant in economics and mathematical finance. Numerical evidence and comparative analyses validate the results and the proposed scheme.

Publisher

MDPI AG

Link

https://www.mdpi.com/2227-7390/12/14/2234/pdf

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