Geodesic
A fast algorithm for the two dimensional HJB equation of stochastic control
ESAIM: Mathematical Modelling and Numerical Analysis , Tome 38 (2004) no. 4, pp. 723-735

Voir la notice de l'article provenant de la source Numdam

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 max ) operations, where p max 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.

DOI : 10.1051/m2an:2004034
Classification : 49L99, 93E20
Keywords: stochastic control, finite differences, viscosity solutions, consistency, HJB equation, Stern-Brocot tree 
@article{M2AN_2004__38_4_723_0,
     author = {Bonnans, J. Fr\'ed\'eric and Ottenwaelter, \'Elisabeth and Zidani, Housnaa},
     title = {A fast algorithm for the two dimensional {HJB} equation of stochastic control},
     journal = {ESAIM: Mathematical Modelling and Numerical Analysis },
     pages = {723--735},
     publisher = {EDP-Sciences},
     volume = {38},
     number = {4},
     year = {2004},
     doi = {10.1051/m2an:2004034},
     mrnumber = {2087732},
     zbl = {1130.93433},
     language = {en},
     url = {http://geodesic.mathdoc.fr/articles/10.1051/m2an:2004034/}
}
TY  - JOUR
AU  - Bonnans, J. Frédéric
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 
PY  - 2004
SP  - 723
EP  - 735
VL  - 38
IS  - 4
PB  - EDP-Sciences
UR  - http://geodesic.mathdoc.fr/articles/10.1051/m2an:2004034/
DO  - 10.1051/m2an:2004034
LA  - en
ID  - M2AN_2004__38_4_723_0
ER  - 
%0 Journal Article
%A Bonnans, J. Frédéric
%A Ottenwaelter, Élisabeth
%A Zidani, Housnaa
%T A fast algorithm for the two dimensional HJB equation of stochastic control
%J ESAIM: Mathematical Modelling and Numerical Analysis 
%D 2004
%P 723-735
%V 38
%N 4
%I EDP-Sciences
%U http://geodesic.mathdoc.fr/articles/10.1051/m2an:2004034/
%R 10.1051/m2an:2004034
%G en
%F M2AN_2004__38_4_723_0
Bonnans, J. Frédéric; Ottenwaelter, Élisabeth; Zidani, Housnaa. A fast algorithm for the two dimensional HJB equation of stochastic control. ESAIM: Mathematical Modelling and Numerical Analysis , Tome 38 (2004) no. 4, pp. 723-735. doi: 10.1051/m2an:2004034

Cité par Sources :