Optimal Systems and Group Invariant Solutions for a Model Arising in Financial Mathematics

Abstract

We consider a bond‐pricing model described in terms of partial differential equations (PDEs). Classical Lie point symmetry analysis of the considered PDEs resulted in a number of point symmetries being admitted. The one‐dimensional optimal system of subalgebras is constructed. Following the symmetry reductions, we determine the group‐invariant solutions.

Key words:

• point symmetries
• optimal systems
• bond‐pricing model
• invariant solutions