The Symmetrical Analysis Method And The Exact Solution Of The Option Pricing Equation And The Camassa-Holm Equation

This paper is concerned with the symmetrical analysis method and the exact solution of the option pricing equation, that is the Black-scholes equation, and the Camassa-Holm equation.In the part of the option pricing equation which has an important position in finance, firstly, the equation’s common form will be deduced. Then using the lie group methods to gain the equation’s the symmetry group and the invariant solution under different symmetry groups. Next using another kind of algebraic method, that is elliptic function expansion method, to analyze its traveling wave solution.In the section of the Camassa-Holm equation that has an important application in natural science and physical phenomena, the Jacobi elliptic function expansion method and the heuristics of the elliptic equation will be used to gain the equation’s traveling wave solutions.