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Convergence of a high-order compact finite difference scheme for a nonlinear Black-Scholes equation
journal contribution
posted on 2023-06-07, 23:11 authored by Bertram Duering, Michel Fournié, Ansgar JüngelA 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.
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Publication status
- Published
Journal
ESAIM: Mathematical Modelling and Numerical AnalysisISSN
0764-583XExternal DOI
Volume
38Page range
359-369Department affiliated with
- Mathematics Publications
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- No
Peer reviewed?
- Yes
Legacy Posted Date
2012-02-06Usage metrics
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