Optimal Timing of Decisions: A General Theory Based on Continuation Values

Building on insights of Jovanovic (1982) and subsequent authors, we develop a comprehensive theory of optimal timing of decisions based around continuation value functions and operators that act on them. Optimality results are provided under general settings, with bounded or unbounded reward functions. This approach has several intrinsic advantages that we exploit in developing the theory. One is that continuation value functions are smoother than value functions, allowing for sharper analysis of optimal policies and more efficient computation. Another is that, for a range of problems, the continuation value function exists in a lower dimensional space than the value function, mitigating the curse of dimensionality. In one typical experiment, this reduces the computation time from over a week to less than three minutes.