Applications of Mortality Durations and Convexities in Natural Hedges
Why this work is in the frame
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Bibliographic record
Abstract
Defining and deriving the mortality durations and convexities of the prices of life insurance and annuity products with respect to an instantaneously proportional change and an instantaneously parallel shift, respectively, in μs (the forces of mortality), qs (the one-year death probabilities), ps (the one-year survival probabilities), ln (μ)s, (q/p)s, and ln (q/p)s, this article applies 24 proposed duration/convexity matching strategies classified into seven groups to determine the weights of two products in an insurance portfolio. The hedging performances of some qualified matching strategies selected as representatives are evaluated by comparing their Value at Risk (VaR) values and variance reduction ratios for a base scenario. We also test some specific scenarios for the population basis risk, model risk, volatility and jump risks, and interest rate risk to see the impacts on the matching strategies. Numerical examples show that some convexity matching strategies overall outperform the others in the VaR value and in the effectiveness of hedging both longevity and mortality risks for two kinds of insurance portfolios.
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Full frame distilled prediction
Teacher imitationNot calibrated prevalence, not ground truth. Human validation pending. Learned from the 10,348 direct Codex labels and 10,348 direct Gemma labels. Candidate is the union of thresholded teacher heads; consensus is their intersection. These outputs are machine_predicted_unvalidated and are not human labels or direct frontier model labels.
Codex and Gemma teacher scores by category
| Category | Codex | Gemma |
|---|---|---|
| Metaresearch | 0.001 | 0.000 |
| Meta-epidemiology (narrow) | 0.000 | 0.000 |
| Meta-epidemiology (broad) | 0.000 | 0.000 |
| Bibliometrics | 0.000 | 0.001 |
| Science and technology studies | 0.000 | 0.001 |
| Scholarly communication | 0.000 | 0.000 |
| Open science | 0.000 | 0.000 |
| Research integrity | 0.000 | 0.000 |
| Insufficient payload (model declined to judge) | 0.000 | 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 it