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Computation
Volume 8
Issue 3
10.3390/computation8030065
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Article

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

by
Winter Sinkala
Department of Mathematical Sciences and Computing, Faculty of Natural Sciences, Walter Sisulu University, Private Bag X1, Mthatha 5117, South Africa
Computation 2020, 8(3), 65; https://doi.org/10.3390/computation8030065
Submission received: 5 June 2020 / Revised: 13 June 2020 / Accepted: 16 June 2020 / Published: 10 July 2020
Versions Notes

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.
Keywords: lie symmetry; conservation law; nonlinear self-adjointness; multiplier method; black-scholes equation lie symmetry; conservation law; nonlinear self-adjointness; multiplier method; black-scholes equation

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MDPI and ACS Style

Sinkala, W. On the Generation of Infinitely Many Conservation Laws of the Black-Scholes Equation. Computation 2020, 8, 65. https://doi.org/10.3390/computation8030065

AMA Style

Sinkala W. On the Generation of Infinitely Many Conservation Laws of the Black-Scholes Equation. Computation. 2020; 8(3):65. https://doi.org/10.3390/computation8030065

Chicago/Turabian Style

Sinkala, Winter. 2020. "On the Generation of Infinitely Many Conservation Laws of the Black-Scholes Equation" Computation 8, no. 3: 65. https://doi.org/10.3390/computation8030065

APA Style

Sinkala, W. (2020). On the Generation of Infinitely Many Conservation Laws of the Black-Scholes Equation. Computation, 8(3), 65. https://doi.org/10.3390/computation8030065

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