  We consider a large family of discrete and continuous time controlled Markov
processes and study an ergodic risk-sensitive minimization problem. Under a
blanket stability assumption, we provide a complete analysis to this problem.
In particular, we establish uniqueness of the value function and verification
result for optimal stationary Markov controls, in addition to the existence
results. We also revisit this problem under a near-monotonicity condition but
without any stability hypothesis. Our results also include policy improvement
algorithms both in discrete and continuous time frameworks.
