We analyse a class of numerical schemes for solving the HJB equation for stochastic control problems, that generalizes the usual finite difference method. The latter is known to be monotonous, and hence valid, only if the scaled covariance matrix is diagonal dominant. We generalize this result by, given the set of neighbouring points allowed to enter in the scheme, showing how to compute the class of covariance matrices that is consistent with this set of points. We perform this computation for several cases in dimension 2 to 4.
Publié le : 2001-07-05
Classification:
CONSISTENCY,
NUMERICAL ANALYSIS OF PARTIAL DIFFERENTIAL EQUATIONS,
STOCHASTIC CONTROL,
FINITE DIFFERENCES,
HAMILTON JACOBI BELLMAN EQUATION,
[INFO.INFO-OH]Computer Science [cs]/Other [cs.OH],
[MATH.MATH-OC]Mathematics [math]/Optimization and Control [math.OC]
@article{Report N°: RR-4162,
author = {Bonnans, J. Frederic and Zidani, Hasnaa},
title = {Consistency of Generalized Finite Difference Schemes for the Stochastic HJB Equation},
journal = {HAL},
volume = {2001},
number = {0},
year = {2001},
language = {en},
url = {http://dml.mathdoc.fr/item/Report N°: RR-4162}
}
Bonnans, J. Frederic; Zidani, Hasnaa. Consistency of Generalized Finite Difference Schemes for the Stochastic HJB Equation. HAL, Tome 2001 (2001) no. 0, . http://gdmltest.u-ga.fr/item/Report%20N%C2%B0:%20RR-4162/