Please use this identifier to cite or link to this item:
Title: Lie Symmetries of (1+2) nonautonomous evolution equations in financial mathematics
Authors: Paliathanasis, Andronikos 
Morris, Richard M. 
Leach, P. G. L. 
Keywords: Lie point symmetries;Financial Mathematics;Prices of commodities;Black-scholes equation
Issue Date: 2016
Publisher: MDPI
Source: Paliathanasis, A.; Morris, R.M. and Leach, P.G.L. 2016. Lie Symmetries of (1+2) nonautonomous evolution equations in financial mathematics. Mathematics. 4(2): 1-14.
Journal: Mathematics (Basel) 
We analyse two classes of (1 + 2) evolution equations which are of special interest in Financial Mathematics, namely the Two-dimensional Black-Scholes Equation and the equation for the Two-factor Commodities Problem. Our approach is that of Lie Symmetry Analysis. We study these equations for the case in which they are autonomous and for the case in which the parameters of the equations are unspecified functions of time. For the autonomous Black-Scholes Equation we find that the symmetry is maximal and so the equation is reducible to the (1 + 2) Classical Heat Equation. This is not the case for the nonautonomous equation for which the number of symmetries is submaximal. In the case of the two-factor equation the number of symmetries is submaximal in both autonomous and nonautonomous cases. When the solution symmetries are used to reduce each equation to a (1 + 1) equation, the resulting equation is of maximal symmetry and so equivalent to the (1 + 1) Classical Heat Equation.
ISSN: 2227-7390 (print)
Appears in Collections:Research Publications (Applied Sciences)

Files in This Item:
File Description SizeFormat
Paliathanasis_Mathematics_Vol4#2_Pgs1-14_2016.pdf798.75 kBAdobe PDFThumbnail
Show full item record

Page view(s)

checked on Jul 14, 2024


checked on Jul 14, 2024

Google ScholarTM


Items in DSpace are protected by copyright, with all rights reserved, unless otherwise indicated.