no. 2
Convergence of a high-order compact finite difference scheme for a nonlinear Black-Scholes equation
ESAIM: Modélisation mathématique et analyse numérique, Tome 38 (2004) no. 2, pp. 359-369.

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.

DOI : 10.1051/m2an:2004018
Classification : 49L25, 65M06, 65M12
Mots clés : high-order compact finite differences, numerical convergence, viscosity solution, financial derivatives 
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     title = {Convergence of a high-order compact finite difference scheme for a nonlinear {Black-Scholes} equation},
     journal = {ESAIM: Mod\'elisation math\'ematique et analyse num\'erique},
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Düring, Bertram; Fournié, Michel; Jüngel, Ansgar. Convergence of a high-order compact finite difference scheme for a nonlinear Black-Scholes equation. ESAIM: Modélisation mathématique et analyse numérique, Tome 38 (2004) no. 2, pp. 359-369. doi : 10.1051/m2an:2004018. http://www.numdam.org/articles/10.1051/m2an:2004018/

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