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Optimal System of Subalgebras and Invariant Solutions for the Black-Scholes EquationPrimeFaces.cw("AccordionPanel","widget_formSmash_some",{id:"formSmash:some",widgetVar:"widget_formSmash_some",multiple:true}); PrimeFaces.cw("AccordionPanel","widget_formSmash_all",{id:"formSmash:all",widgetVar:"widget_formSmash_all",multiple:true});
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2009 (English)Independent thesis Advanced level (degree of Master (Two Years))Student thesis
##### Abstract [en]

##### Place, publisher, year, edition, pages

2009. , p. 69
##### Keywords [en]

Keywords:Black-Scholes Equation, commutators, commutator table, Lie equainvariant solution, optimal system, generators, Airy equation, structure constant
##### National Category

Mathematics Mathematical Analysis Probability Theory and Statistics
##### Identifiers

URN: urn:nbn:se:bth-2817Local ID: oai:bth.se:arkivexBFAC08FDFEDF00FDC12576810045ED21OAI: oai:DiVA.org:bth-2817DiVA, id: diva2:830112
##### Uppsok

Physics, Chemistry, Mathematics

#####

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##### Note

It was an accolade for us to work with Professor Nail.H. Ibrgimov. +46762600953Available from: 2015-04-22 Created: 2009-12-03 Last updated: 2015-06-30Bibliographically approved

The main purpose of this thesis is to use modern goal-oriented adaptive methods of Lie group analysis to construct the optimal sys- tem of Black-Scholes equation. We will show in this thesis how to obtain all invariant solutions by constructing what has now become so popular, optimal system of sub-algebras, the main Lie algebra admit- ted by the Black-Scholes equation. First, we obtain the commutator table of already calculated symmetries of the Black-Scholes equation. We then followed with the calculations of transformation of the gen- erators with the Lie algebra L6 which provides one-parameter group of linear transformations for the operators. Here we make use of the method of Lie equations to solve the partial di®erential equations. Next, we consider the construction of optimal systems of the Black- Scholes equation where the method requires a simpli¯cation of a vector to a general form to each of the transformations of the generators. Further, we construct the invariant solutions for each of the op- timal system. This study is motivated by the analysis of Lie groups which is being taken to another level by ALGA here in Blekinge In- stitute Technology, Sweden. We give a practical and in-depth steps and explanation of how to construct the commutator table, the calcu- lation of the transformation of the generators and the construction of the optimal system as well as their invariant solutions. Keywords: Black-Scholes Equation, commutators, commutator table, Lie equa- tions, invariant solution, optimal system, generators, Airy equation, structure constant,

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