Group Classification (1+2)-dimensional Linear Equation of Asian Options Pricing

TL;DR

This paper classifies symmetries of a class of (1+2)-dimensional linear PDEs used in Asian options pricing, revealing an 8-dimensional Lie algebra and transforming some equations into the Kolmogorov form, enabling exact solutions.

Contribution

It provides a comprehensive group classification for a class of Asian options pricing equations and constructs invariant solutions using symmetry methods.

Findings

Maximum Lie invariance algebra is eight-dimensional.

Equations can be transformed into the Kolmogorov equation.

Invariant solutions are explicitly constructed.

Abstract

We consider a class of (1+2)-dimensional linear partial differential of Asian options pricing. Special cases have been used to models of financial mathematics. We carry out group classification of a class equations. In particular, the maximum dimension Lie invariance algebra within the above class is eight-dimensional. It is shown that an equation with such an algebra can be transformed into the linear Kolmogorov equation with the help of the point transformations of variables. Using the operators of invariance algebra symmetry reduction is carried out and invariant exact solutions are constructed for some equations.