The Lie symmetry algebra of the Longstaff-Schwartz model

TL;DR

This paper applies Lie symmetry analysis to a class of PDEs related to the Longstaff-Schwartz model, identifying their symmetry groups and algebra structures under various parameter conditions.

Contribution

It systematically characterizes the Lie symmetry algebras of the PDEs associated with the model for different parameter values.

Findings

Identified the largest and smallest Lie algebras for the PDEs.

Determined the algebra structures depending on parameters.

Provided a classification of symmetries based on parameter conditions.

Abstract

This study uses Lie's theory of symmetries to compute the symmetry group of a class of partial differential equations parameterized by four constants: $u_{t}=-\left((a-bx)u_{x}+(d-ey)u_{y}+\frac{x}{2}u_{xx}+\frac{y}{2}u_{yy}\right)$; under the various conditions on the constants $a,b,d$ and $e$, we deduce the largest and smallest Lie algebra of symmetries, and we also determined the structure of these algebras.