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Optimal System of Subalgebras and Invariant Solutions for the Black-Scholes Equation
Blekinge Institute of Technology, School of Engineering.
Blekinge Institute of Technology, School of Engineering.
Blekinge Institute of Technology, School of Engineering.
2009 (English)Independent thesis Advanced level (degree of Master (Two Years))Student thesis
Abstract [en]

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,

Place, publisher, year, edition, pages
2009. , 69 p.
Keyword [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: diva2:830112
Uppsok
Physics, Chemistry, Mathematics
Supervisors
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

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CiteExportLink to record
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Citation style
  • apa
  • harvard1
  • ieee
  • modern-language-association-8th-edition
  • vancouver
  • Other style
More styles
Language
  • de-DE
  • en-GB
  • en-US
  • fi-FI
  • nn-NO
  • nn-NB
  • sv-SE
  • Other locale
More languages
Output format
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  • asciidoc
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