Recurrent Neural Networks for Multivariate Loss Reserving and Risk Capital Analysis
Bibliographic record
Abstract
In the property and casualty (P&C) insurance industry, reserves comprise most of a company’s liabilities. These reserves are the best estimates made by actuaries for future unpaid claims. Notably, reserves for different lines of business (LOBs) are related due to dependent events or claims. The actuarial industry and literature have extensively developed both parametric and nonparametric methods to model dependence in loss reserving. However, the use of machine learning tools to capture dependence between loss reserves from multiple LOBs and calculate the aggregated risk capital remains uncharted. This article introduces the use of the Deep Triangle (DT), a recurrent neural network, for multivariate loss reserving, incorporating an asymmetric loss function to combine incremental paid losses of multiple LOBs. The input and output to the DT are the vectors of sequences of incremental paid losses that account for the dependence between and within LOBs. In addition, we utilize generative adversarial networks (GANs) to generate synthetic loss triangles, enabling us to obtain the predictive distribution for reserves and calculate the risk capital. We call the combination of DT for multivariate loss reserving and GAN for risk capital analysis the Extended Deep Triangle (EDT). To speed up the training for DT in EDT, we leverage the DT trained on real data. To illustrate the EDT, we apply and calibrate these methods using data from multiple companies from the National Association of Insurance Commissioners (NAIC) database. To benchmark our method, we compare the EDT to the copula regression models and find that the EDT outperforms the copula regression models in predicting total loss reserve. Furthermore, with the obtained predictive distribution for reserves, we show that risk capitals calculated from the EDT are smaller than that of the copula regression models, suggesting a more considerable diversification benefit. Finally, these findings are also confirmed in a simulation study. Our analysis demonstrates the potential of the EDT in predicting loss reserves and conducting risk capital analysis in practice.
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How this classification was reachedexpand
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 | 0.003 | 0.004 |
| Meta-epidemiology (narrow) | 0.000 | 0.000 |
| Meta-epidemiology (broad) | 0.001 | 0.000 |
| Bibliometrics | 0.001 | 0.002 |
| Science and technology studies | 0.001 | 0.000 |
| Scholarly communication | 0.001 | 0.000 |
| Open science | 0.001 | 0.000 |
| Research integrity | 0.000 | 0.001 |
| 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 itClassification
machine, unvalidatedMachine predicted; a candidate call from one teacher head, 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".