Comparative Statics for Optimal Stopping Problems in Nonstationary Environments

Abstract: How do decisions change with the economic environment and with time? This paper studies general nonstationary stopping problems and provides the methodological tools to answer these questions. First, we identify conditions that ensure a monotone relation between decisions' timing and outcomes. These conditions apply to a prevalent class of economic environments. Second, we develop a theory of monotone comparative statics for stopping problems, offering general and unifying qualitative insights into the decision-maker's value and stopping behavior. We apply our results to models of information acquisition, bankruptcy, irreversible investment, and option pricing to explain documented patterns at odds with current theories.