Optimal claims with fixed payoff structure
Bibliographic record
Abstract
Dybvig (1988) introduced the interesting problem of how to construct in the cheapest possible way a terminal wealth with desired distribution. This idea has induced a series of papers concerning generality, consequences, and applications. As the optimized claims typically follow the trend in the market, they are not useful for investors who wish to use them to protect an existing portfolio. For this reason, Bernard, Moraux, Rüschendorf and Vanduffel (2014b) imposed additional state-dependent constraints as a way of controlling the payoff structure. The present paper extends this work in various ways. In order to obtain optimal claims in general models we allow in this paper for extended contracts. We deal with general multivariate price processes and dispense with several of the regularity assumptions in the previous work (in particular, we omit any continuity assumption). State dependence is modeled by requiring terminal wealth to have a fixed copula with a benchmark wealth. In this setting, we are able to characterize optimal claims. We apply the theoretical results to deal with several hedging and expected utility maximization problems of interest.
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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 | 0.004 | 0.017 |
| Meta-epidemiology (narrow) | 0.001 | 0.001 |
| Meta-epidemiology (broad) | 0.002 | 0.001 |
| Bibliometrics | 0.001 | 0.001 |
| Science and technology studies | 0.001 | 0.002 |
| Scholarly communication | 0.003 | 0.006 |
| Open science | 0.002 | 0.002 |
| Research integrity | 0.003 | 0.003 |
| Insufficient payload (model declined to judge) | 0.004 | 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".