The thesis presents a new method of Symmetry Analysis of the Black-Scholes Merton
Finance Model through modi ed Local one-parameter transformations. We determine
the symmetries of both the one-dimensional and two-dimensional Black-Scholes
equations through a method that involves the limit of in nitesimal ! as it approaches
zero. The method is dealt with extensively in [23]. We further determine an invariant
solution using one of the symmetries in each case. We determine the transformation
of the Black-Scholes equation to heat equation through Lie equivalence transformations.
Further applications where the method is successfully applied include working out
symmetries of both a Gaussian type partial di erential equation and that of a di erential
equation model of epidemiology of HIV and AIDS. We use the new method to
determine the symmetries and calculate invariant solutions for operators providing
them. / Mathematical Sciences / Applied Mathematics / D. Phil. (Applied Mathematics)
| Identifer | oai:union.ndltd.org:netd.ac.za/oai:union.ndltd.org:unisa/oai:umkn-dsp01.int.unisa.ac.za:10500/18410 |
| Date | 09 1900 |
| Creators | Masebe, Tshidiso Phanuel |
| Contributors | Manale, J.M. |
| Source Sets | South African National ETD Portal |
| Language | English |
| Detected Language | English |
| Type | Thesis |
| Format | 1 online resource (viii, 104 leaves) |
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