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A time-changed stochastic control problem and its maximum principle

Nane Erkan, Ni Yinan

Probability and Mathematical Statistics

2021

Vol. 41, Fasc. 2

193--215

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.