Infinite Horizon Stochastic Optimal Control Problems with Running Maximum Cost

Axel Kröner (1, 2) , Athena Picarelli (3) , Hasnaa Zidani (4)

1 Institut für Mathematik [Humboldt]
2 Commands - Control, Optimization, Models, Methods and Applications for Nonlinear Dynamical Systems
3 MI - Mathematical Institute [Oxford]
4 OC - Optimisation et commande

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.

Domaines: Mathématiques [math]; Optimisation et contrôle [math.OC]; Equations aux dérivées partielles [math.AP]; Analyse numérique [math.NA]

Axel Kröner, Athena Picarelli, Hasnaa Zidani. Infinite Horizon Stochastic Optimal Control Problems with Running Maximum Cost. SIAM Journal on Control and Optimization, 2018, 56 (5), pp.3296-3319. ⟨10.1137/17M115253X⟩. ⟨hal-01585766v3⟩