Algebraic aspects of evolution partial differential equation arising in the study of constant elasticity of variance model from financial mathematics
Motsepa Tanki,
Aziz Taha,
Fatima Aeeman,
Khalique Chaudry Masood
Affiliations
Motsepa Tanki
International Institute for Symmetry Analysis and Mathematical Modeling, Department of Mathematical Sciences, North-West University, Mafikeng Campus, Private Bag X 2046, Mmabatho, 2735, South Africa
Aziz Taha
School of Computer, Statistical and Mathematical Sciences, North-West University, Potchefstroom Campus, Private Bag X 6001, Potchefstroom, 2531, South Africa
Fatima Aeeman
International Institute for Symmetry Analysis and Mathematical Modeling, Department of Mathematical Sciences, North-West University, Mafikeng Campus, Private Bag X 2046, Mmabatho, 2735, South Africa
Khalique Chaudry Masood
International Institute for Symmetry Analysis and Mathematical Modeling, Department of Mathematical Sciences, North-West University, Mafikeng Campus, Private Bag X 2046, Mmabatho, 2735, South Africa
The optimal investment-consumption problem under the constant elasticity of variance (CEV) model is investigated from the perspective of Lie group analysis. The Lie symmetry group of the evolution partial differential equation describing the CEV model is derived. The Lie point symmetries are then used to obtain an exact solution of the governing model satisfying a standard terminal condition. Finally, we construct conservation laws of the underlying equation using the general theorem on conservation laws.
