Maximal Use of Central Differencing for Hamilton-Jacobi-Bellman PDEs in Finance

@article{Wang2008MaximalUO,
  title={Maximal Use of Central Differencing for Hamilton-Jacobi-Bellman PDEs in Finance},
  author={Jun Wang and Peter A. Forsyth},
  journal={SIAM J. Numerical Analysis},
  year={2008},
  volume={46},
  pages={1580-1601}
}
In order to ensure convergence to the viscosity solution, the standard method for discretizing HJB PDEs uses forward/backward differencing for the drift term. In this paper, we devise a monotone method which uses central weighting as much as possible. In order to solve the discretized algebraic equations, we have to maximize a possibly discontinuous objective function at each node. Nevertheless, convergence of the overall iteration can be guaranteed. Numerical experiments on two examples from… CONTINUE READING
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