Optimal payoffs under state-dependent constraints
Bibliographic record
Abstract
Most decision theories including expected utility theory, rank dependent utility theory and cumulative prospect theory assume that investors are only interested in the distribution of returns and not in the states of the economy in which income is received. Optimal payoffs have their lowest outcomes when the economy is in a downturn, and this is often at odds with the needs of many investors. We introduce a framework for portfolio selection that permits to deal with state-dependent preferences. We are able to characterize optimal payoffs in explicit form. Some applications in security design are discussed in detail. We extend the classical expected utility optimization problem of Merton to the state-dependent situation and also give some stochastic extensions of the target probability optimization problem. Key-words: Optimal portfolio selection, state-dependent preferences, conditional distribution, hedging, state-dependent constraints. ∗Corresponding author: Carole Bernard, University of Waterloo, 200 University Avenue West, Waterloo, Ontario, N2L3G1, Canada. (email: c3bernar@uwaterloo.ca). Carole Bernard acknowledges support from NSERC. †Franck Moraux, Univ. Rennes 1, 11 rue Jean Mace, 35000 Rennes, France. (email: franck.moraux@univ-rennes1.fr). Franck Moraux acknowledges financial supports from CREM (the CNRS research center) and IAE de Rennes. ‡Ludger Ruschendorf, University of Freiburg, Eckerstrase 1, 79104 Freiburg, Germany. (email: ruschen@stochastik.uni-freiburg.de). §Steven Vanduffel, Vrije Universiteit Brussel, Pleinlaan 2, 1050 Bruxelles, Belgium. (email: steven.vanduffel@vub.ac.be). Steven Vanduffel acknowledges support from BNP Paribas.
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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 | 0.014 |
| Meta-epidemiology (narrow) | 0.001 | 0.001 |
| Meta-epidemiology (broad) | 0.002 | 0.001 |
| Bibliometrics | 0.001 | 0.001 |
| Science and technology studies | 0.000 | 0.001 |
| Scholarly communication | 0.003 | 0.004 |
| Open science | 0.001 | 0.001 |
| Research integrity | 0.002 | 0.002 |
| 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".