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Summary

Old climate models are often evaluated on whether they made correct predictions of global warming. But, if the old models were missing processes that we know now to be important, any correctness of their predictions would have to be attributed to a fortuitous compensation of errors, creating a paradoxical situation. Climate models are also tested for falsifiability by using them to predict the impact of short-term events like volcanic eruptions. But climate models do not exhibit the numeric convergence to a unique solution characteristic of small-scale computational fluid dynamics (CFD) models, like the ones that simulate flow over a wing. Compensating errors may obscure the convergence of individual components of a climate model. Lack of convergence suggests that climate modeling is facing a reducibility barrier, or perhaps even a reducibility limit.

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.

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12 - The Hansen Paradox

Summary

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

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2 results

12 - The Hansen Paradox

Summary

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