Dynamic programming and error estimates for stochastic control problems with maximum cost
2015
Publication type:
Paper in peer-reviewed journals
Journal:
Applied Mathematics and Optimization (AMO, Springer), vol. 71(1), pp. 125--163
HAL:
Abstract:
This work is concerned with stochastic optimal control for a
running maximum cost. A direct approach based on dynamic program-
ming techniques is studied leading to the characterization of the value
function as the unique viscosity solution of a second order Hamilton-
Jacobi-Bellman (HJB) equation with an oblique derivative boundary
condition. A general numerical scheme is proposed and a convergence
result is provided. Error estimates are obtained for the semi-Lagrangian
scheme. These results can apply to the case of lookback options in fi-
nance. Moreover, optimal control problems with maximum cost arise in
the characterization of the reachable sets for a system of controlled sto-
chastic differential equations. Some numerical simulations on examples
of reachable analysis are included to illustrate our approach.
BibTeX:
@article{Bok-Pic-Zid-2015,
author={Olivier Bokanowski and Athena Picarelli and Hasnaa Zidani },
title={Dynamic programming and error estimates for stochastic control
problems with maximum cost },
doi={10.1007/s00245-014-9255-3 },
journal={Applied Mathematics and Optimization (AMO, Springer) },
year={2015 },
volume={71(1) },
pages={125--163},
}