Infinite Horizon Stochastic Optimal Control Problems with Running Maximum Cost

Axel Kröner 1, 2 Athena Picarelli 3 Hasnaa Zidani 4
2 Commands - Control, Optimization, Models, Methods and Applications for Nonlinear Dynamical Systems
UMA - Unité de Mathématiques Appliquées, Inria Saclay - Ile de France, CMAP - Centre de Mathématiques Appliquées - Ecole Polytechnique
Abstract : An infinite horizon stochastic optimal control problem with running maximum cost is considered. The value function is characterized as the viscosity solution of a second-order Hamilton-Jacobi-Bellman (HJB) equation with mixed boundary condition. A general numerical scheme is proposed and convergence is established under the assumptions of consistency, monotonicity and stability of the scheme. These properties are verified for a specific semi-Lagrangian scheme.
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Submitted on : Tuesday, September 25, 2018 - 10:12:31 AM
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Axel Kröner, Athena Picarelli, Hasnaa Zidani. Infinite Horizon Stochastic Optimal Control Problems with Running Maximum Cost. SIAM Journal on Control and Optimization, Society for Industrial and Applied Mathematics, 2018, 56 (5), pp.3296-3319. ⟨10.1137/17M115253X⟩. ⟨hal-01585766v3⟩

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