Bibliographic record
Abstract
Mortality Tables and Rates It is time to get a bit more technical. In this chapter I will cover most of what you need to know about mortality rates and tables in order to appreciate the valuation and pricing of mortality-contingent claims. At various points I will be using basic calculus to express the underlying mathematics. But please don't be discouraged if the material appears somewhat esoteric or theoretical. My main objective is to arrive at a collection of formulas that can be used independently of whether you understand every step of how they were derived. To begin with, the basis of all pension and insurance valuation is the mortality table. A mortality table—perhaps better referred to as a vector or collection of numbers—maps or translates an age group x into a probability of death, q x , during the next year. For example, q 35 is the probability of dying before your 36th birthday, assuming you are alive on your 35th birthday. By definition, 0 ≤ q x ≤ 1 and q N = 1 for some large enough N ≈ 110. Table 3.1 displays a portion of one of the hundreds of different mortality tables. This one is called the RP2000 (where “RP” denotes retirement pension) healthy annuitant mortality table, which is available from the Society of Actuaries, 〈www.soa.org〉. This portion of the table displays conditional death rates from age x = 50 to age x = 105 only in increments of 5 years; the complete table is provided in Chapter 14 of this book.
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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 | 0.001 | 0.002 |
| Meta-epidemiology (narrow) | 0.001 | 0.000 |
| Meta-epidemiology (broad) | 0.001 | 0.001 |
| Bibliometrics | 0.001 | 0.001 |
| Science and technology studies | 0.000 | 0.001 |
| Scholarly communication | 0.002 | 0.002 |
| Open science | 0.002 | 0.001 |
| Research integrity | 0.002 | 0.002 |
| Insufficient payload (model declined to judge) | 0.017 | 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".