Getting Real with Real Options: A Utility–Based Approach for Finite–Time Investment in Incomplete Markets
Bibliographic record
Abstract
Abstract: We apply a utility–based method to obtain the value of a finite–time investment opportunity when the underlying real asset is not perfectly correlated to a traded financial asset. Using the comparison principle for the associated variational inequality, we establish several qualitative properties of the optimal investment boundary, in particular its dependence on correlation and risk aversion. We then use a discrete–time algorithm to calculate the indifference value for this type of real option and present numerical examples for the corresponding investment thresholds. We verify that even in the zero correlation case, whereby none of the risk in the project can be hedged in a financial market, the paradigm of real options can still be applied to value an investment decision, since the opportunity to invest still carries an option value above its net present value. In other words, it is time flexibility itself, more than the possibility of replication, that is the source of the extra value of an investment opportunity. This value, however, quickly erodes at higher levels of risk aversion, and even more so when the project is weakly correlated to financial markets.
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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 | 0.006 | 0.012 |
| Meta-epidemiology (narrow) | 0.001 | 0.001 |
| Meta-epidemiology (broad) | 0.001 | 0.001 |
| Bibliometrics | 0.001 | 0.001 |
| Science and technology studies | 0.001 | 0.003 |
| Scholarly communication | 0.002 | 0.003 |
| Open science | 0.002 | 0.002 |
| Research integrity | 0.002 | 0.002 |
| Insufficient payload (model declined to judge) | 0.005 | 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".