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

TL;DR

This paper analyzes evolution-type equations with time-dependent parameters in financial mathematics using Lie group techniques, providing their symmetry structure and new solutions for exotic options like power options with continuous yield dividends.

Contribution

It introduces a symmetry analysis framework for evolution equations with time-dependent parameters and derives new solutions for exotic options in financial markets.

Findings

Derived the general symmetry structure of evolution-type equations with time-dependent parameters.

Presented new solutions for power options with continuous yield dividends.

Demonstrated the application of Lie group methods to complex financial models.

Abstract

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.