On the Generation of Infinitely Many Conservation Laws of the Black-Scholes Equation

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 sel...

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Bibliographic Details
Published in:Computation 2020-09, Vol.8 (3), p.65
Main Author: Sinkala, Winter
Format: Article
Language:English
Subjects:
black-scholes equation
conservation law
lie symmetry
multiplier method
nonlinear self-adjointness
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Summary: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.
ISSN:2079-3197
2079-3197
DOI:10.3390/computation8030065