  Motivated by a problem of optimal harvesting of natural resources, we study a
control problem for Volterra type dynamics driven by time-changed L\'evy
noises, which are in general not Markovian. To exploit the nature of the noise,
we make use of different kind of information flows within a maximum principle
approach. For this we work with backward stochastic differential equations
(BSDE) with time-change and exploit the non-anticipating stochastic derivative
introduced in [15]. We prove both a sufficient and necessary stochastic maximum
principle.
