Risk sensitive impulse control of non‐Markovian processes

We consider the problem of an optimal stochastic impulse control of non‐Markovian Processes when the expression of the cost functional integrates sensitiveness with respect to the risk. For this class, we try to establish the existence of an optimal strategy. We prove that our impulse control problem could be reduced to an iterative sequence of optimal stopping ones. Basically, the problem is solved using techniques involving the Snell envelope notion.