  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.
