Asymptotics of impulse control problem with multiplicative reward
arXiv:2301.04194 · doi:10.1007/s00245-023-10005-5
Abstract
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.
26 pages