The theory of Markov decision processes focuses on controlled Markov chains in discrete
time. The authors establish the theory for general state and action spaces and at the same …

In this article, we study the design of controllers in the context of stochastic optimal control
under the assumption that the model of the system is not available. This is, we aim to control …

We analyze the effect of small changes in the underlying probabilistic model on the value of
multiperiod stochastic optimization problems and optimal stopping problems. We work in …

We give a general formulation of the utility maximization problem under nondominated
model uncertainty in discrete time and show that an optimal portfolio exists for any utility …

In this paper, we study the learning of safe policies in the setting of reinforcement learning
problems. This is, we aim to control a Markov Decision Process (MDP) of which we do not …

Reinforcement learning consists of finding policies that maximize an expected cumulative
long-term reward in a Markov decision process with unknown transition probabilities and …

We study a robust utility maximization problem in a general discrete-time frictionless market
under quasi-sure no-arbitrage. The investor is assumed to have a random and concave …

We analyze the effect of small changes in the underlying probabilistic model on the value of
multi-period stochastic optimization problems and optimal stopping problems. We work in …

We revisit mean‐risk portfolio selection in a one‐period financial market where risk is
quantified by a positively homogeneous risk measure. We first show that under mild …

This paper proposes two approaches that quantify the exact relationship among viability,
absence of arbitrage, and/or existence of the numéraire portfolio under minimal assumptions …