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Optimal systems of subalgebras for a nonlinear Black-Scholes equation

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  • Maxim Bobrov

Abstract

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.

Suggested Citation

  • Maxim Bobrov, 2009. "Optimal systems of subalgebras for a nonlinear Black-Scholes equation," Papers 0901.2826, arXiv.org.
    • Handle: RePEc:arx:papers:0901.2826
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