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  • About
  • The Global ETD Search service is a free service for researchers to find electronic theses and dissertations. This service is provided by the Networked Digital Library of Theses and Dissertations.
    Our metadata is collected from universities around the world. If you manage a university/consortium/country archive and want to be added, details can be found on the NDLTD website.
1

Multigrid Methods for Hamilton-Jacobi-Bellman and Hamilton-Jacobi-Bellman-Isaacs Equations

Han, Dong January 2011 (has links)
We propose multigrid methods for solving Hamilton-Jacobi-Bellman (HJB) and Hamilton-Jacobi-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 effectively 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 effectiveness 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.
2

Multigrid Methods for Hamilton-Jacobi-Bellman and Hamilton-Jacobi-Bellman-Isaacs Equations

Han, Dong January 2011 (has links)
We propose multigrid methods for solving Hamilton-Jacobi-Bellman (HJB) and Hamilton-Jacobi-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 effectively 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 effectiveness 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.

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