Expected-Shock Substitution Under Censoring: A Case Study in Stochastic Dynamics

Two unlabelled snapshots of a population, taken at different times, do not reveal which individual became which; recovering paths requires assumptions about how individuals move. We study this problem on stock panels, where every stock’s identity is recorded. Identities are hidden while matching the snapshots and revealed only to score the result. This lets us measure what historical information is needed to learn a good motion model. Past snapshots without known matches work almost as well as history with all matches known for a one-day model, and a small set of known matches captures most of the benefit. Known matches matter more when fitting directly over long gaps; a neural model improves 21-day recovery further. Persistent stock attributes such as trading volume strongly affect how well identities can be recovered. The model that best recovers individual identities is not the one that best reproduces outcomes among similar stocks. Matching well between two dates also does not guarantee consistent results when the gap is split at an intermediate date.