Title: Optimal Timing of Decisions: A General Theory Based on Continuation Values,
Abstract: 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.