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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.
In this article we consider the ergodic risk-sensitive control problem for a large class of multidimensional controlled diffusions on the whole space. We study the minimization and maximization problems under either a blanket stability hypothesis, or
We study sequences, parametrized by the number of agents, of many agent exit time stochastic control problems with risk-sensitive cost structure. We identify a fully characterizing assumption, under which each of such control problem corresponds to a
A multiplicative relative value iteration algorithm for solving the dynamic programming equation for the risk-sensitive control problem is studied for discrete time controlled Markov chains with a compact Polish state space, and controlled diffusions
We introduce and treat a class of Multi Objective Risk-Sensitive Markov Decision Processes (MORSMDPs), where the optimality criteria are generated by a multivariate utility function applied on a finite set of emph{different running costs}. To illustr
The paper solves constrained Dynkin games with risk-sensitive criteria, where two players are allowed to stop at two independent Poisson random intervention times, via the theory of backward stochastic differential equations. This generalizes the pre