Multigrid Methods for Hamilton-Jacobi-Bellman and Hamilton-Jacobi-Bellman-Isaacs Equations
نویسنده
چکیده
We propose multigrid methods for solving Hamilton-Jacobi-Bellman (HJB) and HamiltonJacobi-Bellman-Isaacs (HJBI) equations. The methods are based on the full approximation scheme. We propose a damped-relaxation method as smoother for multigrid. In contrast with policy iteration, the relaxation scheme is convergent for both HJB and HJBI equations. We show by local Fourier analysis that the damped-relaxation smoother e ectively reduces high frequency error. For problems where the control has jumps, restriction and interpolation methods are devised to capture the jump on the coarse grid as well as during coarse grid correction. We will demonstrate the e ectiveness of the proposed multigrid methods for solving HJB and HJBI equations arising from option pricing as well as problems where policy iteration does not converge or converges slowly.
منابع مشابه
Multigrid Methods for Second Order Hamilton-Jacobi-Bellman and Hamilton-Jacobi-Bellman-Isaacs Equations
We propose multigrid methods for solving the discrete algebraic equations arising from the discretization of the second order Hamilton–Jacobi–Bellman (HJB) and Hamilton– Jacobi–Bellman–Isaacs (HJBI) equations. We propose a damped-relaxation method as a smoother for multigrid. In contrast with the standard policy iteration, the proposed damped-relaxation scheme is convergent for both HJB and HJB...
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