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

J. Frédéric Bonnans; Élisabeth Ottenwaelter; Housnaa Zidani

ESAIM: Mathematical Modelling and Numerical Analysis (2010)

  • Volume: 38, Issue: 4, page 723-735
  • ISSN: 0764-583X

Abstract

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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(pmax) operations, where pmax is the size of the stencil. The method is based on a walk on the Stern-Brocot tree, and on the related filling of the set of positive semidefinite matrices of size two.

How to cite

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Frédéric Bonnans, J., Ottenwaelter, Élisabeth, and Zidani, Housnaa. "A fast algorithm for the two dimensional HJB equation of stochastic control." ESAIM: Mathematical Modelling and Numerical Analysis 38.4 (2010): 723-735. <http://eudml.org/doc/194236>.

@article{FrédéricBonnans2010,
abstract = { 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(pmax) operations, where pmax is the size of the stencil. The method is based on a walk on the Stern-Brocot tree, and on the related filling of the set of positive semidefinite matrices of size two. },
author = {Frédéric Bonnans, J., Ottenwaelter, Élisabeth, Zidani, Housnaa},
journal = {ESAIM: Mathematical Modelling and Numerical Analysis},
keywords = {Stochastic control; finite differences; viscosity solutions; consistency; HJB equation; Stern-Brocot tree.},
language = {eng},
month = {3},
number = {4},
pages = {723-735},
publisher = {EDP Sciences},
title = {A fast algorithm for the two dimensional HJB equation of stochastic control},
url = {http://eudml.org/doc/194236},
volume = {38},
year = {2010},
}

TY - JOUR
AU - Frédéric Bonnans, J.
AU - Ottenwaelter, Élisabeth
AU - Zidani, Housnaa
TI - A fast algorithm for the two dimensional HJB equation of stochastic control
JO - ESAIM: Mathematical Modelling and Numerical Analysis
DA - 2010/3//
PB - EDP Sciences
VL - 38
IS - 4
SP - 723
EP - 735
AB - 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(pmax) operations, where pmax is the size of the stencil. The method is based on a walk on the Stern-Brocot tree, and on the related filling of the set of positive semidefinite matrices of size two.
LA - eng
KW - Stochastic control; finite differences; viscosity solutions; consistency; HJB equation; Stern-Brocot tree.
UR - http://eudml.org/doc/194236
ER -

References

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