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Proof of the Convergence of the Successive Approximation Algorithm for Numerically Solving the Hamilton-Jacobi-Bellman Equation

Author(s):

F. Herzog, H. Peyrl, H.P. Geering
Conference/Journal:

WSEAS Transactions on Systems, vol. 4, no. 12
Abstract:

This paper proves the convergence of the so-called successive approximation algorithm for numerically solving the Hamilton-Jacobi-Bellman (HJB) equation for stochastic optimal control problems. The successive approximation algorithm overcomes the computational difficulties of the HJB equation, which is a second-order partial differential (PDE) equation coupled with an optimization. The successive approximation separates the optimization problem from the boundary value PDE problem and thus makes the problem solvable by standard numerical techniques. A problem of portfolio optimization, with no known analytical solution, is solved with the numerical algorithm and applied in a real-world case study with US asset market data.

Year:

2005
Type of Publication:

(01)Article
Supervisor:



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% Autogenerated BibTeX entry
@Article { HerPey:2005:IFA_2376,
    author={F. Herzog and H. Peyrl and H.P. Geering},
    title={{Proof of the Convergence of the Successive Approximation
	  Algorithm for Numerically Solving the
	  Hamilton-Jacobi-Bellman Equation}},
    journal={WSEAS Transactions on Systems},
    year={2005},
    volume={4},
    number={12},
    pages={},
    month=dec,
    url={http://control.ee.ethz.ch/index.cgi?page=publications;action=details;id=2376}
}
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