Optimal Timing of Resource Development: A Comparison of Stopping Rules Under Certainty and Uncertainty *
Bibliographic record
Abstract
Timber harvesting and wine storage are the canonical optimal stopping problems under certainty. In these problems asset value is expressed as a function of time, and it is optimal to stop (drink, harvest) the program at the time $ t 0 where the asset's present value is maximized. In another paper (Cairns and Davis 2005) we propose a new stopping rule: the program should be stopped when the asset's value is rising at the continuously compounded rate of discount, r. This r% rule is different from and more general than Hotelling's r% rule for price or net price. While completely general and applicable to all irreversible lumpy investments, it reveals interesting insights about order of extraction. For example, mines are extracted not in order of grade, but in an order created by an equilibrium price path that causes the rise in value of the best mines to fall first to the rate of discount. This explains why least cost mines sometimes are not developed in order, without needing to resort to models with stochastics and ex-post regret. Our stopping rule also shows that the option value of waiting to invest, heralded in the uncertainty literature, is present in the certainty case; one does not terminate a stopping problem if the asset's value is rising at greater than the rate of discount, but only when its rate of rise is about to fall to less than the rate of discount. In the canonical resource problem under uncertainty, resource value is maximized by developing (drinking, harvesting) the asset only after the commodity price rises to some
Fetched live from OpenAlex and de-inverted. Abstracts are not stored in this database: the inverted indexes are 8.6 GB of the frame’s 9.3 GB of text, and the host has 13 GB free.
How this classification was reachedexpand
Full frame machine prediction
Teacher imitationNot calibrated prevalence, not ground truth. Human validation pending. The Gemma side is a direct model label for every work in the frame, read from the title-only record. The Codex side is a classifier learned from the 10,348 direct Codex labels and calibrated to design-weighted sample rates; fields without enough sample support carry no Codex call. Candidate is the union of the two sides; consensus is their intersection. These outputs are machine_predicted_unvalidated and are not human labels.
Distilled classifier scores by category (both heads)
| Category | Codex | Gemma |
|---|---|---|
| Metaresearch | 0.012 | 0.042 |
| Meta-epidemiology (narrow) | 0.001 | 0.001 |
| Meta-epidemiology (broad) | 0.002 | 0.002 |
| Bibliometrics | 0.001 | 0.001 |
| Science and technology studies | 0.001 | 0.002 |
| Scholarly communication | 0.004 | 0.005 |
| Open science | 0.002 | 0.001 |
| Research integrity | 0.002 | 0.002 |
| Insufficient payload (model declined to judge) | 0.003 | 0.000 |
Machine scores (provisional)
The two teacher heads of the student model, read on this work. A score orders the frame for review; it never asserts a category, and the validation status ships verbatim with every row.
Baseline scores from an immature model (maturity gate not passed, 7 training rounds). Scores rank; they never assert a category.
score_only:v0-immature-baseline · verbatim from the scoring run: score_only means the number may rank works, and no category label ships from itClassification
machine, unvalidatedMachine predicted; a candidate call from one source (direct Gemma or distilled Codex), not a consensus.
How this classification was reached, model by model and score by score, is at the end of the page under "How this classification was reached".