Explicit description of all deflators for market models under random horizon with applications to NFLVR
Bibliographic record
Abstract
This paper considers an initial market model, specified by its underlying assets $S$ and its flow of information $\mathbb F$, and an arbitrary random time $τ$ which might not be an $\mathbb F$-stopping time. As the death time and the default time (that $τ$ might represent) can be seen when they occur only, the progressive enlargement of $\mathbb F$ with $τ$ sounds tailor-fit for modelling the new flow of information $\mathbb G$ that incorporates both $\mathbb F$ and $τ$. In this setting of informational market, the first principal goal resides in describing as explicitly as possible the set of all deflators for $(S^τ, \mathbb G)$, while the second principal goal lies in addressing the No-Free-Lunch-with-Vanishing-Risk concept (NFLVR hereafter) for $(S^τ, \mathbb G)$. Besides this direct application to NFLVR, the set of all deflators constitutes the dual set of all "admissible" wealth processes for the stopped model $(S^τ,\mathbb G)$, and hence it is vital in many hedging and pricing related optimization problems. Thanks to the results of Choulli et al. [7], on martingales classification and representation for progressive enlarged filtration, our two main goals are fully achieved in different versions, when the survival probability never vanishes. The results are illustrated on the two particular cases when $(S,\mathbb F)$ follows the jump-diffusion model and the discrete-time model.
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 | 0.006 | 0.010 |
| Meta-epidemiology (narrow) | 0.001 | 0.001 |
| Meta-epidemiology (broad) | 0.002 | 0.003 |
| Bibliometrics | 0.002 | 0.001 |
| Science and technology studies | 0.001 | 0.002 |
| Scholarly communication | 0.003 | 0.007 |
| Open science | 0.002 | 0.003 |
| Research integrity | 0.003 | 0.006 |
| Insufficient payload (model declined to judge) | 0.006 | 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 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".