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Full-Text Articles in Other Mathematics
Discrete-Time Control With Non-Constant Discount Factor, Héctor Jasso-Fuentes, José-Luis Menaldi, Tomás Prieto-Rumeau
Discrete-Time Control With Non-Constant Discount Factor, Héctor Jasso-Fuentes, José-Luis Menaldi, Tomás Prieto-Rumeau
Mathematics Faculty Research Publications
This paper deals with discrete-time Markov decision processes (MDPs) with Borel state and action spaces, and total expected discounted cost optimality criterion. We assume that the discount factor is not constant: it may depend on the state and action; moreover, it can even take the extreme values zero or one. We propose sufficient conditions on the data of the model ensuring the existence of optimal control policies and allowing the characterization of the optimal value function as a solution to the dynamic programming equation. As a particular case of these MDPs with varying discount factor, we study MDPs with stopping, …
On Optimal Stopping And Impulse Control With Constraint, J. L. Menaldi, M. Robin
On Optimal Stopping And Impulse Control With Constraint, J. L. Menaldi, M. Robin
Mathematics Faculty Research Publications
The optimal stopping and impulse control problems for a Markov-Feller process are considered when the controls are allowed only when a signal arrives. This is referred to as control problems with constraint. In [28, 29, 30], the HJB equation was solved and an optimal control (for the optimal stopping problem, the discounted impulse control problem and the ergodic impulse control problem, respectively) was obtained, under suitable conditions, including a setting on a compact metric state space. In this work, we extend most of the results to the situation where the state space of the Markov process is locally compact.