9 research outputs found
Ergodic Risk-Sensitive Control for Regime-Switching Diffusions
In this article, we study the ergodic risk-sensitive control problem for
controlled regime-switching diffusions. Under a blanket stability hypothesis,
we solve the associated nonlinear eigenvalue problem for weakly coupled systems
and characterize the optimal stationary Markov controls via a suitable
verification theorem. We also consider the near-monotone case and obtain the
existence of principal eigenfunction and optimal stationary Markov controls
Asymptotics of impulse control problem with multiplicative reward
We consider a long-run impulse control problem for a generic Markov process with a multiplicative reward functional. We construct a solution to the associated Bellman equation and provide a verification result. The argument is based on the probabilistic properties of the underlying process combined with the Krein-Rutman theorem applied to the specific non-linear operator. Also, it utilises the approximation of the problem in the bounded domain and with the help of the dyadic time-grid