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arXiv · 1403.1217

Semi-Lagrangian schemes for linear and fully non-linear Hamilton-Jacobi-Bellman equations

Kristian Debrabant·Espen R. Jakobsen
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Abstract

We consider the numerical solution of Hamilton-Jacobi-Bellman equations arising in stochastic control theory. We introduce a class of monotone approximation schemes relying on monotone interpolation. These schemes converge under very weak assumptions, including the case of arbitrary degenerate diffusions. Besides providing a unifying framework that includes several known first order accurate schemes, stability and convergence results are given, along with two different robust error estimates. Finally, the method is applied to a super-replication problem from finance.

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Kristian Debrabant, Espen R. Jakobsen. 2014-03-05. Semi-Lagrangian schemes for linear and fully non-linear Hamilton-Jacobi-Bellman equations. https://arxiv.org/abs/1403.1217

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