Dynamic Programming and Error Estimates for Stochastic Control Problems with Maximum Cost - Inria - Institut national de recherche en sciences et technologies du numérique Accéder directement au contenu
Article Dans Une Revue Applied Mathematics and Optimization Année : 2014

Dynamic Programming and Error Estimates for Stochastic Control Problems with Maximum Cost

Résumé

This work is concerned with stochastic optimal control for a running maximum cost. A direct approach based on dynamic programming 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 finance. Moreover, optimal control problems with maximum cost arise in the characterization of the reachable sets for a system of controlled stochastic differential equations. Some numerical simulations on examples of reachable analysis are included to illustrate our approach.
Fichier principal
Vignette du fichier
Max_Cost.pdf (569.35 Ko) Télécharger le fichier
Origine : Fichiers produits par l'(les) auteur(s)

Dates et versions

hal-00931025 , version 1 (14-01-2014)
hal-00931025 , version 2 (11-05-2014)

Identifiants

  • HAL Id : hal-00931025 , version 1

Citer

Olivier Bokanowski, Athena Picarelli, Hasnaa Zidani. Dynamic Programming and Error Estimates for Stochastic Control Problems with Maximum Cost. Applied Mathematics and Optimization, 2014. ⟨hal-00931025v1⟩
883 Consultations
776 Téléchargements

Partager

Gmail Facebook X LinkedIn More