Log-Optimal Portfolio without NFLVR: Existence, Complete Characterization, and Duality
Bibliographic record
Abstract
This paper addresses the log-optimal portfolio, which is the portfolio with finite expected log-utility that maximizes the expected logarithm utility from terminal wealth, for an arbitrary general semimartingale model. The most advanced literature on this topic elaborates existence and characterization of this portfolio under the no-free-lunch-with-vanishing-risk (NFLVR for short) assumption, while there are many financial models violating NFLVR and admitting the log-optimal portfolio. In this paper, we provide a complete and explicit characterization of the log-optimal portfolio and its associated optimal deflator, give necessary and sufficient conditions for their existence, and elaborate their duality no matter what the market model. Furthermore, our characterization gives an explicit and direct relationship between log-optimal and numéraire portfolios without changing the probability or the numéraire.
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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 | 0.001 | 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 | 0.000 |
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 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".