Title of article :
EXPANDED LIE GROUP TRANSFORMATIONS AND SIMILARITY REDUCTIONS FOR THE CELEBRITY BLACK-SCHOLES EQUATION IN FINANCE
Author/Authors :
POLAT, R., Yasar University - Faculty of Science and Letters - Department of Mathematics, Turkey , OZIS, T., Ege University - Science Faculty - Department of Mathematics, Turkey
Abstract :
In this study, we consider continuous groups of transformations acting on expanded space of variables, which includes the equation parameters in addition to independent and dependent variables. We have shown that the use of the expanded transformations and similarity reductions enable us to reduce celebrity Black-Scholes equation to formerly unknown reduced (target) ordinary differential equations. Moreover, the obtained reduced ordinary equations are used to find the exact solution of celebrity Black-Scholes equation in finance.
Keywords :
Black , Scholes Equation , Continuous Groups of Transformations , Expanded Lie Group Transformations , Reduction Form
Journal title :
applied and computational mathematics
