Bibliographic record
Abstract
This paper considers a pair (F,τ), where F is a filtration representing the “public” flow of information that is available to all agents over time, and τ is a random time that might not be an F-stopping time. This setting covers the case of a credit risk framework, where τ models the default time of a firm or client, and the setting of life insurance, where τ is the death time of an agent. It is clear that random times cannot be observed before their occurrence. Thus, the larger filtration, G, which incorporates F and makes τ observable, results from the progressive enlargement of F with τ. For this informational setting, governed by G, we analyze the optimal stopping problem in three main directions. The first direction consists of characterizing the existence of the solution to this problem in terms of F-observable processes. The second direction lies in deriving the mathematical structures of the value process of this control problem, while the third direction singles out the associated optimal stopping problem under F. These three aspects allow us to deeply quantify how τ impacts the optimal stopping problem and are also vital for studying reflected backward stochastic differential equations that arise naturally from pricing and hedging of vulnerable claims.
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How this classification was reachedexpand
Full frame distilled prediction
Teacher imitationNot calibrated prevalence, not ground truth. Human validation pending. Learned from the 10,348 direct Codex labels and 10,348 direct Gemma labels. Candidate is the union of thresholded teacher heads; consensus is their intersection. These outputs are machine_predicted_unvalidated and are not human labels or direct frontier model labels.
Codex and Gemma teacher scores by category
| Category | Codex | Gemma |
|---|---|---|
| Metaresearch | 0.000 | 0.000 |
| Meta-epidemiology (narrow) | 0.000 | 0.000 |
| Meta-epidemiology (broad) | 0.000 | 0.000 |
| Bibliometrics | 0.000 | 0.000 |
| Science and technology studies | 0.000 | 0.000 |
| Scholarly communication | 0.000 | 0.000 |
| Open science | 0.000 | 0.000 |
| Research integrity | 0.000 | 0.000 |
| Insufficient payload (model declined to judge) | 0.000 | 0.001 |
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 teacher head, 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".