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Convergence of a high-order compact finite difference scheme for a nonlinear Black-Scholes equation
journal contributionposted on 2023-06-07, 23:11 authored by Bertram Duering, Michel Fournié, Ansgar Jüngel
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.
JournalESAIM: Mathematical Modelling and Numerical Analysis
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