Some Solvable Stochastic Control Problems With Delay

We consider optimal harvesting of systems described by stochastic differential equations with delay. We focus on those situations where the value function of the harvesting problem depends on the initial path of the process in a simple way, namely through its value at 0 and through some weighted averages

A verification theorem of variational inequality type is proved. This is applied to solve explicitly some classes of optimal harvesting delay problems