Optimal systems of subalgebras for a nonlinear Black-Scholes equation
| dc.creator | Bobrov, Maxim | |
| dc.date | 2009-01-19 | |
| dc.date.accessioned | 2026-07-07T12:39:16Z | |
| dc.date.available | 2026-07-07T12:39:16Z | |
| dc.description | The main object of our study is a four dimensional Lie algebra which describes the symmetry properties of a nonlinear Black-Scholes model. This model implements a feedback effect which is typical for an illiquid market. The structure of the Lie algebra depends on one parameter, i.e. we have to do with a one-parametric family of algebras. We provide a classification of these algebras using Patera--Winternitz method. Optimal systems of one-, two- and three- dimensional subalgebras are described for the family of symmetry algebras of the nonlinear Black-Scholes equation. The optimal systems give us the possibility to describe a complete set of invariant solutions to the equation. | |
| dc.identifier | https://arxiv.org/abs/0901.2826 | |
| dc.identifier | http://arxiv.org/abs/0901.2826 | |
| dc.identifier.uri | http://salesiana.dossiersoluciones.com/handle/123456789/219048 | |
| dc.subject | Computational Finance | |
| dc.title | Optimal systems of subalgebras for a nonlinear Black-Scholes equation | |
| dc.type | text |