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anriseth / HJBSolver.jl

General solver for Hamilton-Jacobi-Bellman equations
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Use second-order finite differences when possible #4

Open anriseth opened 7 years ago

anriseth commented 7 years ago

Make the code use second-order finite differences for the v_x term whenever possible. We can for example follow the approach from the paper below.

http://epubs.siam.org/doi/abs/10.1137/060675186

@article{wang2008maximal,
  title={Maximal use of central differencing for Hamilton-Jacobi-Bellman PDEs in finance},
  author={Wang, J and Forsyth, Peter A},
  journal={SIAM Journal on Numerical Analysis},
  volume={46},
  number={3},
  pages={1580--1601},
  year={2008},
  publisher={SIAM}
}
anriseth commented 7 years ago

This may cause the objective function to be non-smooth/discontinuous in the controller. This would cause issues with Optim, so it might be best to only do with the "constant policy timestepping" method.