Numerical solution of the Hamilton-Jacobi-Bellman equation for stochastic optimal control problems

Authors:
Helfried Peyrl;Florian Herzog;Hans P. Geering
Affiliations:
Measurement and Control Laboratory, Swiss Federal Institute of Technology Zurich, Züric, Switzerland;Measurement and Control Laboratory, Swiss Federal Institute of Technology Zurich, Züric, Switzerland;Measurement and Control Laboratory, Swiss Federal Institute of Technology Zurich, Züric, Switzerland
Venue:
CONTROL'05 Proceedings of the 2005 WSEAS international conference on Dynamical systems and control
Year:
2005

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Abstract

This paper provides a numerical solution of the Hamilton-Jacobi-Bellman (HJB) equation for stochastic optimal control problems. The computation's difficulty is due to the nature of the HJB equation being a second-order partial differential equation which is coupled with an optimization. By using a successive approximation algorithm, the optimization gets separated from the boundary value problem. This makes the problem solveable by standard numerical methods. For a problem of portfolio optimization where no analytical solution is known, the numerical methods is applied and its usefulness demonstrated.