Document Type



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, as well as the corresponding optimal stopping times and contact set. We show applications to switching MDPs models and, in particular, we study a pollution accumulation problem.


Dynamical Systems | Other Mathematics


This is a post-peer-review, pre-copyedit version of an article published in Mathematical Methods of Operations Research. The final authenticated version is available online at:

Supported by Grant MTM2016-75497-P from the Spanish Ministerio de Economía y Competitividad.