A Penalty Method for the Numerical Solution of Hamilton-Jacobi-Bellman (HJB) Equations in Finance

@article{Witte2011APM,
  title={A Penalty Method for the Numerical Solution of Hamilton-Jacobi-Bellman (HJB) Equations in Finance},
  author={J. Witte and C. Reisinger},
  journal={SIAM J. Numer. Anal.},
  year={2011},
  volume={49},
  pages={213-231}
}
We present a simple and easy-to-implement method for the numerical solution of a rather general class of Hamilton-Jacobi-Bellman (HJB) equations. In many cases, classical finite difference discretizations can be shown to converge to the unique viscosity solutions of the considered problems. However, especially when using fully implicit time stepping schemes with their desirable stability properties, one is still faced with the considerable task of solving the resulting nonlinear discrete system… Expand
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