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Vol. 48 No. 4 (2022)
Serdica Mathematical Journal

Articles

Application of Lie symmetries to solving modified Black-Scholes equation

https://doi.org/10.55630/serdica.2022.48.219-234

Published 15-10-2022

  • Realeboha Ramoeletsi
    • ,
  • Bosiu Kaibe
    • ,
  • Ngaka J. Nchejane

Realeboha Ramoeletsi
National University of Lesotho

Bosiu Kaibe
National University of Lesotho

Ngaka J. Nchejane
National University of Lesotho

Abstract

We perform Lie symmetry analysis on the modified Black-Scholes model described as a partial differential equation (PDE). As a result, a new complete Lie symmetry group and infinitesimal generators of the one-dimensional modified fractional Black-Scholes model are derived. Furthermore, we compute a family of exact invariant solutions that constitute the modified fractional Black-Scholes model using the associated infinitesimal generators and the corresponding similarity reduction equations. Using known solutions, more solutions are generated via group point transformations.

2020 Mathematics Subject Classification:

35-XX

Keywords

Lie point symmetries, modified Black-Scholes, financial mathematics, Lie algebra, invariant solution

Full text

Author Details

Realeboha Ramoeletsi

Department of Mathematics and Computer Science
National University of Lesotho
Maseru Roma 180, Lesotho
e-mail: realeboharamoeletsi@gmail.com

Bosiu Kaibe

Department of Mathematics and Computer Science
National University of Lesotho
Maseru Roma 180, Lesotho
e-mail: bosiukaibe@yahoo.com

Ngaka J. Nchejane

Department of Mathematics and Computer Science
National University of Lesotho
Maseru Roma 180, Lesotho
e-mail: jn.nchejane@nul.ls

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