Endre søk

Referera
Referensformat
• apa
• ieee
• modern-language-association-8th-edition
• vancouver
• Annet format
Fler format
Språk
• de-DE
• en-GB
• en-US
• fi-FI
• nn-NO
• nn-NB
• sv-SE
• Annet språk
Fler språk
Utmatningsformat
• html
• text
• asciidoc
• rtf
Optimal System of Subalgebras and Invariant Solutions for the Black-Scholes Equation
Blekinge Tekniska Högskola, Sektionen för ingenjörsvetenskap.
Blekinge Tekniska Högskola, Sektionen för ingenjörsvetenskap.
Blekinge Tekniska Högskola, Sektionen för ingenjörsvetenskap.
2009 (engelsk)Independent thesis Advanced level (degree of Master (Two Years))Oppgave
##### 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,

2009. , s. 69
##### Emneord [en]
Keywords:Black-Scholes Equation, commutators, commutator table, Lie equainvariant solution, optimal system, generators, Airy equation, structure constant
##### Identifikatorer
Lokal ID: oai:bth.se:arkivexBFAC08FDFEDF00FDC12576810045ED21OAI: oai:DiVA.org:bth-2817DiVA, id: diva2:830112
##### Uppsök
Physics, Chemistry, Mathematics
##### Veileder
It was an accolade for us to work with Professor Nail.H. Ibrgimov. +46762600953Tilgjengelig fra: 2015-04-22 Laget: 2009-12-03 Sist oppdatert: 2015-06-30bibliografisk kontrollert

#### Open Access i DiVA

fulltekst(422 kB)266 nedlastinger
##### Filinformasjon
Fil FULLTEXT01.pdfFilstørrelse 422 kBChecksum SHA-512
Type fulltextMimetype application/pdf

#### Søk utenfor DiVA

Totalt: 266 nedlastinger
Antall nedlastinger er summen av alle nedlastinger av alle fulltekster. Det kan for eksempel være tidligere versjoner som er ikke lenger tilgjengelige
urn-nbn

#### Altmetric

urn-nbn
Totalt: 129 treff

Referera
Referensformat
• apa
• ieee
• modern-language-association-8th-edition
• vancouver
• Annet format
Fler format
Språk
• de-DE
• en-GB
• en-US
• fi-FI
• nn-NO
• nn-NB
• sv-SE
• Annet språk
Fler språk
Utmatningsformat
• html
• text
• asciidoc
• rtf