Optimal systems of subalgebras for a nonlinear Black-Scholes equation
AbstractThe 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.
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Bibliographic InfoPaper provided by arXiv.org in its series Papers with number 0901.2826.
Date of creation: Jan 2009
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Web page: http://arxiv.org/
This paper has been announced in the following NEP Reports:
- NEP-ALL-2009-09-26 (All new papers)
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