In this presentation we study the investment problem when both the demand and the investment costs are stochastic. We assume that the processes are independent, and both are modeled using geometric Brownian motion with exogenous jumps driven by independent Poisson processes. We use a real options approach, leading to an optimal stopping problem. Due to the multi-uncertainty, we propose a method to solve explicitly the problem, and we prove that this method leads exactly to the solution of the optimization problem.

Joint work with Rita Pimentel.