Convergence of a high-order compact finite difference scheme for a nonlinear Black-Scholes equation

Düring, Bertram, Fournié, Michel and Jüngel, Ansgar (2004) Convergence of a high-order compact finite difference scheme for a nonlinear Black-Scholes equation. ESAIM: Mathematical Modelling and Numerical Analysis, 38. pp. 359-369. ISSN 0764-583X

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Abstract

A high-order compact finite difference scheme for a fully nonlinear parabolic differential equation is analyzed. The equation arises in the modeling of option prices in financial markets with transaction costs. It is shown that the finite difference solution converges locally uniformly to the unique viscosity solution of the continuous equation. The proof is based on a careful study of the discretization matrices and on an abstract convergence result due to Barles and Souganides.

Item Type: Article
Schools and Departments: School of Mathematical and Physical Sciences > Mathematics
Depositing User: Bertram During
Date Deposited: 06 Feb 2012 19:31
Last Modified: 14 Jun 2012 09:24
URI: http://sro.sussex.ac.uk/id/eprint/20986
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