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Advances in Mathematical Physics - Volume 2015 2015, Article ID 361785, 9 pages -

Research ArticleDepartment of Mathematical Sciences and Computing, Faculty of Natural Sciences, Walter Sisulu University, Private Bag X1, Mthatha 5117, South Africa

Received 8 June 2015; Revised 7 July 2015; Accepted 25 July 2015

Academic Editor: Stephen C. Anco

Copyright © 2015 Winter Sinkala and Tembinkosi F. Nkalashe. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.


A first-order feedback model of option pricing consisting of a coupled system of two PDEs, a nonliner generalised Black-Scholes equation and the classical Black-Scholes equation, is studied using Lie symmetry analysis. This model arises as an extension of the classical Black-Scholes model when liquidity is incorporated into the market. We compute the admitted Lie point symmetries of the system and construct an optimal system of the associated one-dimensional subalgebras. We also construct some invariant solutions of the model.

Autor: Winter Sinkala and Tembinkosi F. Nkalashe



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