More on the Origin of Financial Economics: Early Contributions to Joint Life Annuity Valuation
Bibliographic record
Abstract
The origin of modern financial economics can be traced to early discounted expected value solutions for the price of life annuities. In contrast to the single life annuity valuations attributed to de Witt and Halley, the computational complexity of joint life annuity valuation posed difficulties. Following a brief review of various joint life annuity specifications, a history of joint life annuity issuance and valuation in northern Europe from the 13th to the mid-18th century is provided. With this background, the 1671 correspondence from de Witt to Hudde on possible methods for valuing joint life annuities is detailed. These methods are contrasted with the geometric method described in Halley (1693); providing impetus for examination of the analytical approximations developed by de Moivre and Simpson.
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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 | 0.003 | 0.009 |
| Meta-epidemiology (narrow) | 0.001 | 0.000 |
| Meta-epidemiology (broad) | 0.001 | 0.001 |
| Bibliometrics | 0.003 | 0.004 |
| Science and technology studies | 0.001 | 0.008 |
| Scholarly communication | 0.005 | 0.012 |
| Open science | 0.001 | 0.002 |
| Research integrity | 0.002 | 0.006 |
| Insufficient payload (model declined to judge) | 0.008 | 0.002 |
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".