Risk-sensitive stochastic impulse control problems with random coefficients and execution delays

Abstract This paper studies a risk-sensitive control problem on a finite time horizon with execution delays where the reward and intervention cost functions can belong to a large class of stochastic processes. In particular, the intervention cost function is modeled by right-continuous and left-limited processes that are quasi-left continuous. A probabilistic approach is adopted in this setting based on the Snell envelope concept. We characterize recursively optimal solutions to risk-sensitive control problems by recasting the control problem as an iterative optimal stopping problem. We show the existence of an optimal strategy and establish the connection between the approximation scheme and the associated total expected reward.