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DOE OSTI · 22470060

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

Bokanowski, Olivier·Picarelli, Athena·Zidani, Hasnaa
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Abstract

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.

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71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSICS97 MATHEMATICS AND COMPUTINGBOUNDARY CONDITIONSCOMPUTERIZED SIMULATIONCONVERGENCEDIFFERENTIAL EQUATIONSDYNAMIC PROGRAMMINGLAGRANGIAN FUNCTIONMATHEMATICAL SOLUTIONSOPTIMAL CONTROLSTOCHASTIC PROCESSESVISCOSITY

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Bokanowski, Olivier, Picarelli, Athena, Zidani, Hasnaa. 2015-02-15. Dynamic Programming and Error Estimates for Stochastic Control Problems with Maximum Cost. https://doi.org/10.1007/s00245-014-9255-3

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