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.

[1] Al-Azemi F., Calin O. Asian Options with Harmonic Average. Appl. Math. Inf. Sci. 2015, 9 (6), 2803–2811.
[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] 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] 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] 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.
[6] Ibragimov N. X. (ed.) CRC Handbook of Lie Group Analysis of Differential Equations. CRC Press, Boca Raton, 1994.
[7] Lahno V. I., Spichak S. V., Stogniy V. I. Symmetry Analysis of Evolution Type Equations. Institute of Mathematics of NAS of Ukraine, Kyiv, 2002. (in Ukrainian)
[8] Nikitin A. G., Popovych R. O. Group classification nonlinear Schrodinger equations. Ukr. Math. J. 2001, 53 (8), 1255–1265.
[9] Ovsiannikov L. V. Group Analysis of Differential Equations. Academic Press, New York, 1982.
[10] Ovsiannikov L. V. Group properties of nonlinear heat equation. Dokl. AN SSSR 1959, 125 (3), 492–495. (in Russian)
[11] Rassokha I., Serov M., Spichak S., Stogniy V. Group classification of a class of generalized nonlinear Kolmogorov equations and exact solutions. J. Math. Phys. 2018, 59 (7), 071514.
[12] Spichak S. V., Stogniy V. I. Symmetry classification and exact solutions of the Kramers equation. J. Math. Phys. 1998, 39 (6), 3505–3510.
[13] Spichak S. V., Stogniy V. I., Kopas I. M. Symmetry properties and exact solutions of (2+1)-dimensional linear equations of pricing of Asian options. Proceedings of Institute of Mathematscs of NAS of Ukraine 2019, 16 (1), 164–173. (in Ukrainian)
[14] Vaneeva O., Karadzhov Yu., Sophocleous C. Group analysis of a class of nonlinear Kolmogorov equations. Lie Theory and Its Applications in Physics, Springer Proc. Math. Stat., Springer, Singapore 2016, 191, 349–360.