Abstract
Construction of conservation laws of differential equations is an essential part of the mathematical study of differential equations. In this paper we derive, using two approaches, general formulas for finding conservation laws of the Black-Scholes equation. In one approach, we exploit nonlinear self-adjointness and Lie point symmetries of the equation, while in the other approach we use the multiplier method. We present illustrative examples and also show how every solution of the Black-Scholes equation leads to a conservation law of the same equation.
Highlights
An important study of mathematical models described by differential equations concerns construction of the inherent conservation laws of equations
In the case of partial differential equations (PDEs), conservation laws can be used to search for potential symmetries, which in turn lead to new solutions of the equations via admitted nonlocal symmetries
We are able to obtain the explicit formulas for conservation laws of any nonlinearly self-adjoint Equation (2) that admits symmetries
Summary
An important study of mathematical models described by differential equations concerns construction of the inherent conservation laws of equations. The second method used is the direct method proposed by Anco and Bluman in 1996 [3,5] This method essentially reduces the construction of conservation laws to solving a system of linear determining equations similar to that for finding Lie point symmetries. An explicit formula is derived which yields a conservation law for each solution of the determining system Using this method we characterise conservation laws of the Black-Scholes equation in terms of solutions of the associated adjoint equation.
Sign-in/Register to view highlights & summary Sign-in/Register to access full text options 
Free) 
Talk to us
Join us for a 30 min session where you can share your feedback and ask us any queries you have
Schedule a call
