A time-changed stochastic control problem and its maximum principle

This paper studies a time-changed stochastic control problem, where the underlying stochastic process is a Lévy noise time-changed by an inverse subordinator. We establish a maximum principle for the time-changed stochastic control problem. We also prove the existence and uniqueness of the corresponding time-changed backward stochastic differ- ential equation involved in the stochastic control problem. Some examples are provided for illustration.