Inlämning av Examensarbete / Submission of Thesis

Zahid Hussain; Muhammad Sulaiman; Edward K. E. Sackey 2009:07, pp. 69. ING/School of Engineering, 2009.

The work

Url (don't fill in this field it is used to fool spam robots): Zahid Hussain, Muhammad Sulaiman, Edward K. E. Sackey zahidmaths@yahoo.com, edsac77@yahoo.co.nz Optimal System of Subalgebras and Invariant Solutions for the Black-Scholes Equation 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, Mathematics\Analysis Mathematics\General Mathematics\Probability and Statistics Keywords:Black-Scholes Equation, commutators, commutator table, Lie equainvariant solution, optimal system, generators, Airy equation, structure constant

Publication info

Dokument id / Document id: Mathematical Modelling and Simulation 12/03/2009 Masterarbete/Master's Thesis (120 credits)

Context

 Handledare / Supervisor: PROF. NAIL H. IBRAGIMOV nail.ibragimov@bth.se PROF. NAIL H. IBRAGIMOV Blekinge Institute of Technology ING/School of Engineering +46 455 38 50 00 It was an accolade for us to work with Professor Nail.H. Ibrgimov. +46762600953

Files & Access

Bifogad uppsats fil(er) / Files attached: thesis.pdf (431 kB, öppnas i nytt fönster)