Optimal stochastic impulse control with random coefficients and execution delay

We study a general impulse control problem with execution delay, which means that there is a time lag between a decision and the timing of its execution. Since the classical approach is not applicable when the underlying dynamics of the controlled system is a general adapted stochastic process, we suggest general probabilistic tools, namely the Snell envelope and reflected backward stochastic differential equations to model the profitability of the controller, and find the related optimal strategy.