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

Bertram Düring; Michel Fournié; Ansgar Jüngel

ESAIM: Mathematical Modelling and Numerical Analysis (2010)

- Volume: 38, Issue: 2, page 359-369
- ISSN: 0764-583X

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topDüring, Bertram, Fournié, Michel, and Jüngel, Ansgar. "Convergence of a high-order compact finite difference scheme for a nonlinear Black–Scholes equation." ESAIM: Mathematical Modelling and Numerical Analysis 38.2 (2010): 359-369. <http://eudml.org/doc/194218>.

@article{Düring2010,

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.
},

author = {Düring, Bertram, Fournié, Michel, Jüngel, Ansgar},

journal = {ESAIM: Mathematical Modelling and Numerical Analysis},

keywords = {High-order compact finite differences; numerical convergence;
viscosity solution; financial derivatives.; viscosity solutions; financial derivatives},

language = {eng},

month = {3},

number = {2},

pages = {359-369},

publisher = {EDP Sciences},

title = {Convergence of a high-order compact finite difference scheme for a nonlinear Black–Scholes equation},

url = {http://eudml.org/doc/194218},

volume = {38},

year = {2010},

}

TY - JOUR

AU - Düring, Bertram

AU - Fournié, Michel

AU - Jüngel, Ansgar

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

JO - ESAIM: Mathematical Modelling and Numerical Analysis

DA - 2010/3//

PB - EDP Sciences

VL - 38

IS - 2

SP - 359

EP - 369

AB -
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.

LA - eng

KW - High-order compact finite differences; numerical convergence;
viscosity solution; financial derivatives.; viscosity solutions; financial derivatives

UR - http://eudml.org/doc/194218

ER -

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