Numerical solution using radial basis functions for multidimensional fractional partial differential equations of type Black-Scholes

TL;DR

This paper presents a meshless radial basis function method for numerically solving multidimensional time-space-fractional Black-Scholes equations, demonstrating flexibility and improved matrix conditioning for complex financial models.

Contribution

It introduces a novel radial basis function approach tailored for multidimensional fractional PDEs in finance, addressing matrix conditioning issues.

Findings

Effective in solving multidimensional fractional PDEs

Reduces condition number of involved matrices

Applicable to complex financial modeling scenarios

Abstract

The aim of this paper is to solve numerically, using the meshless method via radial basis functions, time-space-fractional partial differential equations of type Black-Scholes. The time-fractional partial differential equation appears in several diffusion problems used in physics and engineering applications, and models subdiffusive and superdiffusive behavior of the prices at the stock market. This work shows the flexibility of the radial basis function scheme to solve multidimensional problems with several types of nodes and it also shows how to reduce the condition number of the matrices involved.