# 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

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topFrédéric 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 -

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