Author:
Spichak S.,Stogniy V.,Kopas I.
Abstract
A group classification of one class of (2+1)-dimensional linear equations of Asian options pricing was carried out. As a result, the kernel of maximal invariance algebras and continuous equivalence transformations of this class of equations were found. Using equivalence transformations, all non-equivalent subclasses of equations that have an invariance algebra wider than the kernel of maximal invariance algebras are selected. For each such subclass of equations, Lie algebras of symmetry operators of dimensions four, five, and eight are found.
Publisher
Yuriy Fedkovych Chernivtsi National University
Subject
Computer Science Applications,History,Education
Reference14 articles.
1. [1] Al-Azemi F., Calin O. Asian Options with Harmonic Average. Appl. Math. Inf. Sci. 2015, 9 (6), 2803–2811.
2. [2] Barucci E., Polidoro S., Vespri V. Some Results on Partial Differential Equations and Asian options. Math. Models and Methods in Appl. Sci. 2001, 11 (3), 475–497.
3. [3] Demetriou E., Ivanova N. M., Sophocleous C. Group analysis of (2+1)- and (3+1)-dimensional diffusion-convection equations. J. Math. Anal. Appl. 2008, 348 (1), 55–65.
4. [4] Dorodnitsyn V. A., Knyazeva I. V., Svirschevsky S. R. Group properties of the heat equation with a source in two-dimensional and three-dimensional cases. Differential Equations 1983, 19 (7), 1215–1223. (in Russian)
5. [5] Elwakil S. A., Zahran M. À., Sabry R. Group classification and symmetry reduction of a (2+1)- dimensional diffusion-advection equation. J. Appl. Math. Phys. 2005, 56 (6), 986–999.