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

Authors :
Tao Liu
Zixiao Zhao
Shiyi Ling
Heyang Chao
Hasan Fattahi Nafchi
Stanford Shateyi
Source :
Mathematics, Vol 12, Iss 14, p 2234 (2024)
Publication Year :
2024
Publisher :
MDPI AG, 2024.

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.

Details

Language :
English
ISSN :
22277390
Volume :
12
Issue :
14
Database :
Directory of Open Access Journals
Journal :
Mathematics
Publication Type :
Academic Journal
Accession number :
edsdoj.f6b79d1f59a44ea3b5a9ebaa396e64d0
Document Type :
article
Full Text :
https://doi.org/10.3390/math12142234