Incomplete Markets, Knightian Uncertainty, and Irreversible Investment

Abstract

The problem of irreversible investment with idiosyncratic risk is studied by interpreting market incompleteness as a source of Knightian uncertainty over the appropriate discount factor. Maxmin utility over multiple priors is used to solve the irreversible investment problem. The notion of priors with kappa-ignorance are used to analyse finitely lived options. For infinitely lived options the notion of constant kappa-ignorance is introduced. For these sets of density generators the corresponding optimal stopping problem is solved for general (in-)finite horizon optimal stopping problems driven by geometric Brownian motions. It is argued that an increase in the level of ambiguity delays investment, whereas an increase in the degree of market completeness can have a non-monotonic effect.