Dynamic Programming and Error Estimates for Stochastic Control Problems with Maximum Cost
- Laboratoire Jacques-Louis Lions, Université Paris-Diderot (Paris 7) UFR de Mathématiques - Bât. Sophie Germain (France)
- Projet Commands, INRIA Saclay & ENSTA ParisTech (France)
- Unité de Mathématiques appliquées (UMA), ENSTA ParisTech (France)
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.
- OSTI ID:
- 22470060
- Journal Information:
- Applied Mathematics and Optimization, Journal Name: Applied Mathematics and Optimization Journal Issue: 1 Vol. 71; ISSN 0095-4616
- Country of Publication:
- United States
- Language:
- English
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