Knightian Uncertainty, k-Ignorance, and Optimal Timing

We investigate within a continuous time setting how Knightian uncertainty characterized by k-ignorance affects the optimal timing policies of a risk-neutral and uncertainty averse investor in the case where the exercise payoff is monotonic. We prove that increased Knightian uncertainty unambiguously decreases the value of the optimal timing policy of an uncertainty averse investor. We also show that higher Knightian uncertainty accelerates timing by shrinking the continuation region whenever the termination payoff is independent of Knightian uncertainty. If this independence condition is not fulfilled, then our results indicate that higher Knightian uncertainty may decelerate optimal timing.