Conditions for Exact Hedging in an Unconstrained Regime-Switching Market Model
Bibliographic record
Abstract
In an earlier contribution “Unconstrained hedging within a regime-switching market model” (Sixth Indian Control Conference, Hyderabad, December 18-20, 2019) the authors address the problem of unconstrained hedging in a financial market model which includes regime-switching, in the sense that the basic sources of randomness in the market model are a standard multidimensional Brownian motion, together with an independent finite-state Markov chain (the latter process models so-called regime-switches, which are occasional “large-scale” random changes in the market parameters, as opposed to the persistent “small-scale” changes in the market parameters which are driven by the Brownian motion). Under these conditions the market model is “incomplete”, and the best that one can do is establish existence of a least initial wealth along with an investment strategy for which the corresponding wealth process almost-surely majorizes - but generally does not equal - the contingent claim at close of trade (in this case the claim is said to be “super-hedged”). The goal of the present work is to complement this result and introduce natural conditions on the regime- switching model under which there exists a least initial wealth and an investment strategy such that the corresponding wealth almost-surely equals the contingent claim at close of trade (so that the claim is “exactly hedged”). Our motivation is primarily in the works of Cvitanic and Karatzas (1993) and El Karoui and Quenez (1995) who address the case where incompleteness in the market model arises from portfolio constraints rather than regime-switching.
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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 | 0.001 | 0.002 |
| Scholarly communication | 0.002 | 0.005 |
| Open science | 0.001 | 0.003 |
| Research integrity | 0.002 | 0.003 |
| Insufficient payload (model declined to judge) | 0.008 | 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".