Elham Motiefar: Analysis and Application of Lie Group Theory on PDE in Finance

The purpose of this study was to examine the connection between theory and practice and investigating the corresponding process in between. Another aim was to find out the connection between mathematical models and financial solutions. Because of this goal, in this thesis a financial problem was considered, the components of the problem were analysed and in order to solve such kind of problems, the method with the name "Lie group analysis" based on the symmetry analysis was chosen. Also different situation of this problem were examined in the study to obtain the reductions arising from Lie symmetry of a partial differential equation (PDE) to an ordinary differential equation (ODE), which was easier to solve in comparison with solving the PDE.