Copula-Based Risk Aggregation and the Significance of Reinsurance
Bibliographic record
Abstract
Insurance companies need to calculate solvency capital requirements in order to ensure that they can meet their future obligations to policyholders and beneficiaries. The solvency capital requirement is a risk management tool essential for addressing extreme catastrophic events that result in a high number of possibly interdependent claims. This paper studies the problem of aggregating the risks coming from several insurance business lines and analyses the effect of reinsurance on the level of risk. Our starting point is to use a hierarchical risk aggregation method which was initially based on two-dimensional elliptical copulas. We then propose the use of copulas from the Archimedean family and a mixture of different copulas. Our results show that a mixture of copulas can provide a better fit to the data than an individual copula and consequently avoid over- or underestimation of the capital requirement of an insurance company. We also investigate the significance of reinsurance in reducing the insurance company’s business risk and its effect on diversification. The results show that reinsurance does not always reduce the level of risk, but can also reduce the effect of diversification for insurance companies with multiple business lines.
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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 | 0.009 | 0.048 |
| 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 | 0.001 | 0.001 |
| Research integrity | 0.001 | 0.002 |
| Insufficient payload (model declined to judge) | 0.001 | 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 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".