Timing decisions under model uncertainty

We study the effect of ambiguity on timing decisions. An agent faces a stopping problem with an uncertain stopping payoff and a stochastic time limit. The agent is unsure about the correct model quantifying the uncertainty and seeks to maximize her payoff guarantee over a set of plausible models. As time passes and the agent updates, the worst-case model used to evaluate a given strategy can change, creating a problem of dynamic inconsistency. We characterize the stopping behavior in this environment and show that, while the agent's myopic incentives are fragile to small changes in the set of considered models, the best consistent plan from which no future self has incentives to deviate is robust.