HJBSolver

General solver for Hamilton-Jacobi-Bellman equations.

Solve one-dimensional HJB equations of the form

v_t + \sup_{a\in A}\{ b(t,x,a)*v_x + \frac{1}{2}\sigma(t,x,a)^2v_{xx} + f(t,x,a)\}= 0

HJBSolver implements two Finite Difference solvers based on the algorithms described in forsyth2007numerical:

• Policy iteration: Run a local optimisation for the policy on each time-step.
• Piecewise constant policy timestepping: Approximate the policy function from a discrete set of values.

TODO:

• Show how to use it
• Warn about crappy code

Citations

@article{forsyth2007numerical,
  title={Numerical methods for controlled Hamilton-Jacobi-Bellman PDEs in finance},
  author={Forsyth, Peter A and Labahn, George},
  journal={Journal of Computational Finance},
  volume={11},
  number={2},
  pages={1},
  year={2007}
}