Symmetry structure and solution of evolution-type equations with time dependent parameters in financial Mathematics

Mathematical models with time dependent parameters are of great interest in financial Mathematics because they capture real life scenarios in the financial market. In this study, via the Lie group technique, we analyse evolution-type equations with time dependent parameters and give the general symmetry structure of these equations. In addition, we illustrate this method by looking at an example of exotic options called the power options. Our model parameters are time dependent and the option gives a continuous yield dividend at different time intervals. We present new solutions, satisfying the boundary conditions, to this important problem.