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

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