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 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.
Infinite Horizon Stochastic Optimal Control Problems with Running Maximum Cost
Picarelli, Athena
;
2018-01-01
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 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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