Center for Mathematical Economics Working Papers No. 634
In this paper, we study an irreversible investment problem under Knightian uncertainty. In a general framework, in which Knightian uncertainty is modeled through a set of multiple priors, we prove existence and uniqueness of the optimal investment plan, and derive necessary and sufficient conditions for optimality. This allows us to construct the optimal policy in terms of the solution to a stochastic backward equation under the worst- case scenario. In a time-homogeneous setting - where risk is driven by a geometric Brownian motion and Knightian uncertainty is realized through a so-called "k-ignorance" - we are able to provide the explicit form of the optimal irreversible investment plan.
irreversible investment Knightian uncertainty singular stochastic control base capacity policy first-order conditions for optimality backward equations