Jump to content
Change search PrimeFaces.cw("Fieldset","widget_formSmash_search",{id:"formSmash:search",widgetVar:"widget_formSmash_search",toggleable:true,collapsed:true,toggleSpeed:500,behaviors:{toggle:function(ext) {PrimeFaces.ab({s:"formSmash:search",e:"toggle",f:"formSmash",p:"formSmash:search"},ext);}}});
$(function(){PrimeFaces.cw("Dialog","citationDialog",{id:"formSmash:upper:j_idt218",widgetVar:"citationDialog",width:"800",height:"600"});});
$(function(){PrimeFaces.cw("ImageSwitch","widget_formSmash_j_idt1013",{id:"formSmash:j_idt1013",widgetVar:"widget_formSmash_j_idt1013",fx:"fade",speed:500,timeout:8000},"imageswitch");});
#### Open Access in DiVA

####

##### By organisation

School of Engineering
On the subject

MathematicsMathematical AnalysisProbability Theory and Statistics
#### Search outside of DiVA

GoogleGoogle Scholar$(function(){PrimeFaces.cw('Chart','widget_formSmash_j_idt1203_0_downloads',{id:'formSmash:j_idt1203:0:downloads',type:'bar',responsive:true,data:[[7,20,15,10,9,16,6,6,11,7]],title:"Downloads of File (FULLTEXT01)",axes:{yaxis: {label:"",min:0,max:30,renderer:$.jqplot.LinearAxisRenderer,tickOptions:{angle:0}},xaxis: {label:"",renderer:$.jqplot.CategoryAxisRenderer,tickOptions:{angle:-90}}},series:[{label:'diva2:830112'}],ticks:["Feb -23","Mar -23","Apr -23","May -23","Jun -23","Jul -23","Aug -23","Sep -23","Oct -23","Nov -23"],orientation:"vertical",barMargin:3,datatip:true,datatipFormat:"<span style=\"display:none;\">%2$d</span><span>%2$d</span>"},'charts');}); Total: 801 downloads$(function(){PrimeFaces.cw("OverlayPanel","widget_formSmash_j_idt1206",{id:"formSmash:j_idt1206",widgetVar:"widget_formSmash_j_idt1206",target:"formSmash:downloadLink",showEvent:"mousedown",hideEvent:"mousedown",showEffect:"blind",hideEffect:"fade"});}); findCitings = function() {PrimeFaces.ab({s:"formSmash:j_idt1209",f:"formSmash",u:"formSmash:citings",pa:arguments[0]});};$(function() {findCitings();}); $(function(){PrimeFaces.cw('Chart','widget_formSmash_visits',{id:'formSmash:visits',type:'bar',responsive:true,data:[[5,2,3,3,2,2,1,14,1,7]],title:"Visits for this publication",axes:{yaxis: {label:"",min:0,max:20,renderer:$.jqplot.LinearAxisRenderer,tickOptions:{angle:0}},xaxis: {label:"",renderer:$.jqplot.CategoryAxisRenderer,tickOptions:{angle:-90}}},series:[{label:'diva2:830112'}],ticks:["Jan -23","Feb -23","Mar -23","Apr -23","May -23","Jun -23","Jul -23","Sep -23","Oct -23","Nov -23"],orientation:"vertical",barMargin:3,datatip:true,datatipFormat:"<span style=\"display:none;\">%2$d</span><span>%2$d</span>"},'charts');}); Total: 276 hits
$(function(){PrimeFaces.cw("Dialog","citationDialog",{id:"formSmash:lower:j_idt1302",widgetVar:"citationDialog",width:"800",height:"600"});});

CiteExport$(function(){PrimeFaces.cw("TieredMenu","widget_formSmash_upper_j_idt197",{id:"formSmash:upper:j_idt197",widgetVar:"widget_formSmash_upper_j_idt197",autoDisplay:true,overlay:true,my:"left top",at:"left bottom",trigger:"formSmash:upper:exportLink",triggerEvent:"click"});}); $(function(){PrimeFaces.cw("OverlayPanel","widget_formSmash_upper_j_idt198_j_idt200",{id:"formSmash:upper:j_idt198:j_idt200",widgetVar:"widget_formSmash_upper_j_idt198_j_idt200",target:"formSmash:upper:j_idt198:permLink",showEffect:"blind",hideEffect:"fade",my:"right top",at:"right bottom",showCloseIcon:true});});

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});
function selectAll()
{
var panelSome = $(PrimeFaces.escapeClientId("formSmash:some"));
var panelAll = $(PrimeFaces.escapeClientId("formSmash:all"));
panelAll.toggle();
toggleList(panelSome.get(0).childNodes, panelAll);
toggleList(panelAll.get(0).childNodes, panelAll);
}
/*Toggling the list of authorPanel nodes according to the toggling of the closeable second panel */
function toggleList(childList, panel)
{
var panelWasOpen = (panel.get(0).style.display == 'none');
// console.log('panel was open ' + panelWasOpen);
for (var c = 0; c < childList.length; c++) {
if (childList[c].classList.contains('authorPanel')) {
clickNode(panelWasOpen, childList[c]);
}
}
}
/*nodes have styleClass ui-corner-top if they are expanded and ui-corner-all if they are collapsed */
function clickNode(collapse, child)
{
if (collapse && child.classList.contains('ui-corner-top')) {
// console.log('collapse');
child.click();
}
if (!collapse && child.classList.contains('ui-corner-all')) {
// console.log('expand');
child.click();
}
}
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

#####

PrimeFaces.cw("AccordionPanel","widget_formSmash_j_idt494",{id:"formSmash:j_idt494",widgetVar:"widget_formSmash_j_idt494",multiple:true});
##### Supervisors

PrimeFaces.cw("AccordionPanel","widget_formSmash_j_idt500",{id:"formSmash:j_idt500",widgetVar:"widget_formSmash_j_idt500",multiple:true});
#####

PrimeFaces.cw("AccordionPanel","widget_formSmash_j_idt506",{id:"formSmash:j_idt506",widgetVar:"widget_formSmash_j_idt506",multiple:true});
##### 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,

urn-nbn$(function(){PrimeFaces.cw("Tooltip","widget_formSmash_j_idt1231",{id:"formSmash:j_idt1231",widgetVar:"widget_formSmash_j_idt1231",showEffect:"fade",hideEffect:"fade",showDelay:500,hideDelay:300,target:"formSmash:altmetricDiv"});});

CiteExport$(function(){PrimeFaces.cw("TieredMenu","widget_formSmash_lower_j_idt1284",{id:"formSmash:lower:j_idt1284",widgetVar:"widget_formSmash_lower_j_idt1284",autoDisplay:true,overlay:true,my:"left top",at:"left bottom",trigger:"formSmash:lower:exportLink",triggerEvent:"click"});}); $(function(){PrimeFaces.cw("OverlayPanel","widget_formSmash_lower_j_idt1285_j_idt1287",{id:"formSmash:lower:j_idt1285:j_idt1287",widgetVar:"widget_formSmash_lower_j_idt1285_j_idt1287",target:"formSmash:lower:j_idt1285:permLink",showEffect:"blind",hideEffect:"fade",my:"right top",at:"right bottom",showCloseIcon:true});});