Symmetry reductions of some non-linear 1+1 D and 2+1 D black-scholes models

dc.contributor.author	Seoka, Nonhlanhla
dc.date.accessioned	2016-09-19T14:09:14Z
dc.date.available	2016-09-19T14:09:14Z
dc.date.issued	2016-09-19
dc.description	A dissertation submitted to the Faculty of Science, University of the Witwatersrand, Johannesburg, in fulfilment of requirements for the degree of Master of Science. May 30, 2016.
dc.description.abstract	In this dissertation, we consider a number of modi ed Black-Scholes equations being either non-linear or given in higher dimensions. In particular we focus on the non-linear Black-Scholes equation describing option pricing with hedging strategies in one case, and two dimensional models in the other. Classical Lie point symmetry techniques are employed in an attempt to construct exact solutions. Some large symmetry algebras are admitted. We proceeded by determining the one dimensional optimal systems of sub-algebras for the admitted Lie algebras. The elements of the optimal systems are used to reduce the number of variables by one. In some cases, exact solutions are constructed. For the cases for which exact solutions are di cult to construct, we employed the numerical solutions. Some simulations are observed and interpreted	en_ZA
dc.description.librarian	MT2016	en_ZA
dc.identifier.uri	http://hdl.handle.net/10539/21084
dc.language.iso	en	en_ZA
dc.subject.lcsh	Symmetry (Mathematics)
dc.subject.lcsh	Mathematical models.
dc.title	Symmetry reductions of some non-linear 1+1 D and 2+1 D black-scholes models	en_ZA
dc.type	Thesis	en_ZA

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