Decomposition of risk based on the Martingale Representation Theorem for annuity and insurance portfolios
Bibliographic record
Abstract
Numerous methods have been proposed throughout the literature for decomposing liabilities into risk factors. Such analysis is of great importance because it allows for explaining the impact of each source of risk in relation to the total risk, and thus it allows actuaries to have a certain degree of control over uncertainties. In an insurance context, such sources usually consist of the mortality risk, represented in this paper by the systematic and by the unsystematic mortality risk, and of the investment risk. The objective of this thesis is to consider the Martingale Representation Theorem (MRT) introduced by Schilling et al., (2015) for such risk decomposition, because this method allows for a detailed analysis of the influence of each source of risk. The proposed dynamic models used in this thesis are the Lee-Carter model for the mortality rates and, the arbitrage-free Nelson-Siegel (AFNS) models for the interest rates. These models are necessary in providing accuracy by improving the overall predictive performance. Once, the risk decomposition has been achieved, quantifying the relative importance of each risk factor under different risk measurements is then proceeded. The numerical results are based on annuities and insurances portfolios. It is found that for extended coverage periods, investment risk represents most of the risk while for shorter terms, the unsystematic mortality risk takes larger importance. It is also found that the systematic mortality risk is almost negligible.
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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 | 0.009 |
| Meta-epidemiology (narrow) | 0.001 | 0.000 |
| Meta-epidemiology (broad) | 0.001 | 0.002 |
| Bibliometrics | 0.002 | 0.001 |
| Science and technology studies | 0.000 | 0.001 |
| Scholarly communication | 0.002 | 0.002 |
| Open science | 0.001 | 0.001 |
| Research integrity | 0.001 | 0.003 |
| Insufficient payload (model declined to judge) | 0.004 | 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".