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A fast algorithm for the two dimensional HJB equation of stochastic control

J. Frédéric Bonnans;  Élisabeth Ottenwaelter;  Housnaa Zidani — 2004

ESAIM: Mathematical Modelling and Numerical Analysis - Modélisation Mathématique et Analyse Numérique

This paper analyses the implementation of the generalized finite differences method for the HJB equation of stochastic control, introduced by two of the authors in [Bonnans and Zidani, SIAM J. Numer. Anal. 41 (2003) 1008–1021]. The computation of coefficients needs to solve at each point of the grid (and for each control) a linear programming problem. We show here that, for two dimensional problems, this linear programming problem can be solved in O ( p m a x ) operations, where p m a x is the size of the stencil....

A fast algorithm for the two dimensional HJB equation of stochastic control

J. Frédéric Bonnans;  Élisabeth Ottenwaelter;  Housnaa Zidani — 2010

ESAIM: Mathematical Modelling and Numerical Analysis

This paper analyses the implementation of the generalized finite differences method for the HJB equation of stochastic control, introduced by two of the authors in [Bonnans and Zidani, (2003) 1008–1021]. The computation of coefficients needs to solve at each point of the grid (and for each control) a linear programming problem. We show here that, for two dimensional problems, this linear programming problem can be solved in operations, where  ...

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