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EnglishThis 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.
Dynamic Programming and Error Estimates for Stochastic Control Problems with Maximum Cost / Bokanowski, Olivier; Picarelli, Athena; Zidani, Hasnaa. - In: APPLIED MATHEMATICS AND OPTIMIZATION. - ISSN 0095-4616. - STAMPA. - 71:1(2014), pp. 125-163.
| Titolo: | Dynamic Programming and Error Estimates for Stochastic Control Problems with Maximum Cost |
| Autori: | |
| Data di pubblicazione: | 2014 |
| Rivista: | |
| Citazione: | Dynamic Programming and Error Estimates for Stochastic Control Problems with Maximum Cost / Bokanowski, Olivier; Picarelli, Athena; Zidani, Hasnaa. - In: APPLIED MATHEMATICS AND OPTIMIZATION. - ISSN 0095-4616. - STAMPA. - 71:1(2014), pp. 125-163. |
| Handle: | http://hdl.handle.net/11562/979346 |
| Appare nelle tipologie: | 01.01 Articolo in Rivista |
File in questo prodotto:
| File | Descrizione | Tipologia | Licenza | |
|---|---|---|---|---|
| Bokanowski_Picarelli_Zidani_revised.pdf | Documento in Post-print |  | Open Access Visualizza/Apri |
http://hdl.handle.net/11562/979346
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