anriseth / hjbsolver.jl Goto Github PK

Extend the code to handle equations of the form

v_t+\sup_{a\in A}\{b*v_x + 1/2*\sigma^2*v_{xx} - c*v + f\} = 0

Currently only Dirichlet boundaries are allowed.
Generalise to e.g. using the limiting value of the PDE expression on certain parts of the boundary.

Improve the interface to choose between the "constant policy timestepping" and the "policy iteration" solvers.

1D and 2D use K differently: 1D specifies K which creates K+1 spatial points but in 2D K is the number of points.

Generalise the code so that we can deal with n-dimensional HJB equations.
Initially with a diagonal diffusion operator.

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}
}

2D tests are too slow for Travis

Currently the value and policy arrays are stored in backward time, so v[:, 1] represents the value function at t=T and v[:, end] represents the value function at t=0.

Redo this so we get it the right way.

Currently the policy iteration approach loops over each x-value and optimises the control only at that position.
Is it possible (and faster) to run a larger optimisation over the controls on all x-values instead? Maybe by summing together hamiltonian(i,j) for all the indices i (and j in 2D)?