A Lie symmetry analysis of the Black-scholes Merton finance model through modified local one-parameter transformations

The thesis presents a new method of Symmetry Analysis of the Black-Scholes Merton Finance Model through modi ed Local one-parameter transformations. We determine the symmetries of both the one-dimensional and two-dimensional Black-Scholes equations through a method that involves the limit of in nitesimal ! as it approaches zero. The method is dealt with extensively in [23]. We further determine an invariant solution using one of the symmetries in each case. We determine the transformation of the Black-Scholes equation to heat equation through Lie equivalence transformations. Further applications where the method is successfully applied include working out symmetries of both a Gaussian type partial di erential equation and that of a di erential equation model of epidemiology of HIV and AIDS. We use the new method to determine the symmetries and calculate invariant solutions for operators providing them.Mathematical SciencesApplied MathematicsD. Phil. (Applied Mathematics