End-to-end reinsurance analytics pipeline combining Extreme Value Theory, treaty structuring, and program optimization using real insurance data (freMTPL2 — 678,013 French Motor TPL policies).
Built as a portfolio project targeting quantitative roles at reinsurers (Swiss Re, Munich Re, IRB Brasil RE) and P&C insurers.
streamlit run app/streamlit_app.py
Most junior data science portfolios stop at model training. This project replicates the actual workflow of a reinsurance analyst:
- Characterize the portfolio — identify heavy-tail behavior using exceedance curves and Q-Q plots
- Model extreme events — fit Generalized Pareto Distribution (GPD) using Peaks Over Threshold; calculate VaR and TVaR at 99.5% (Solvency II standard)
- Structure reinsurance treaties — implement Quota Share, Excess of Loss, and Stop Loss; compare their impact on the loss distribution
- Optimize the program — use differential evolution to find the treaty structure that minimizes
Premium + Cost of Capital × VaR 99.5% - Stress test — evaluate program robustness under catastrophe, frequency shock, severity inflation, and combined stress scenarios
The Hill estimator confirms a heavy tail with index α ≈ 0.9 (below the finite-variance boundary of 2). The GPD shape parameter ξ = 1.001 indicates Pareto-type tail behavior — a key insight for treaty structuring.
| Return Period | Expected Loss |
|---|---|
| 1-in-10 years | 3,222 |
| 1-in-50 years | 10,034 |
| 1-in-100 years | 18,557 |
| 1-in-200 years | 35,614 |
| 1-in-500 years | 86,825 |
The XL 400k xs 100k structure reduces VaR 99.9% by 45% while leaving VaR 99.5% unchanged — a direct consequence of the Pareto-type tail (ξ > 1). This is the correct analytical finding, not a bug.
The optimizer finds the Aggregate Stop Loss attachment that minimizes total cost. The efficient frontier shows the classic U-shape: lower attachment reduces capital cost but raises premium faster.
The reinsurance program truncates the right tail of the annual aggregate distribution. VaR 99.5% falls from 19.2M to 15.3M — a 20.1% capital relief.
| Scenario | Capital Relief |
|---|---|
| Base | 20.1% |
| Frequency shock (+30%) | 15.6% |
| Severity inflation (+20%) | 16.8% |
| Catastrophe (1% years × 3-8x) | 5.9% |
| Combined shock | 5.6% |
The program protects well against frequency and severity shocks but provides limited relief in catastrophe scenarios because the Stop Loss limit (3.86M) is exhausted when annual losses spike to 65M+.
Reinsurers measure capital on an annual aggregate basis (Solvency II SCR, internal models). A per-occurrence XL treaty with retention 50k–200k barely affects the annual VaR of a high-frequency / moderate-severity portfolio like freMTPL2 — the 19M annual loss is composed of ~5,000 small claims, not a few large ones. This project correctly uses Monte Carlo simulation to build the annual aggregate distribution before optimizing capital.
Layer 1: Per-occurrence XL 950k xs 50k → cuts individual large claims
Layer 2: Aggregate Stop Loss → directly reduces annual VaR 99.5%
Attachment: 1.29x mean annual loss
Limit: 0.32x mean annual loss
Differential evolution (global optimizer) minimizes:
Total Cost = Burning Cost × 1.15 + Stop Loss Premium × 1.25 + 8% × VaR_99.5%(annual retained)
reinsurance-portfolio-optimization/
│
├── README.md
├── requirements.txt
│
├── data/
│ ├── raw/ # freMTPL2freq.csv, freMTPL2sev.csv (auto-downloaded)
│ └── processed/
│ └── claims_cleaned.csv # generated by notebook 01
│
├── notebooks/
│ ├── 01_data_exploration.ipynb
│ ├── 02_extreme_value_theory.ipynb
│ ├── 03_treaty_structuring.ipynb
│ └── 04_optimization.ipynb
│
├── src/
│ ├── data_loader.py # freMTPL2 loader with Hugging Face fallback
│ ├── evt_models.py # GPD fitting, VaR/TVaR, Hill estimator
│ ├── treaty_simulator.py # QuotaShare, ExcessOfLoss, StopLoss, Program
│ └── optimization.py # Monte Carlo simulation + differential evolution
│
├── app/
│ └── streamlit_app.py # Interactive dashboard (5 pages)
│
└── results/
├── figures/ # All plots (generated by notebooks)
└── tables/ # risk_metrics.csv, stress_test_results.csv
git clone https://github.com/arthurpmotta02/reinsurance-portfolio-optimization.git
cd reinsurance-portfolio-optimization
python -m venv venv
venv\Scripts\activate # Windows
# source venv/bin/activate # Linux/Mac
pip install -r requirements.txtjupyter notebookOpen and run each notebook:
01_data_exploration.ipynb— downloads freMTPL2 and generatesclaims_cleaned.csv02_extreme_value_theory.ipynb— GPD fitting, VaR/TVaR, return periods03_treaty_structuring.ipynb— Quota Share, XL, full program04_optimization.ipynb— Monte Carlo + Stop Loss optimization + stress testing
cd app
streamlit run streamlit_app.pyfreMTPL2 (French Motor Third-Party Liability) — the benchmark dataset for actuarial data science.
| File | Rows | Description |
|---|---|---|
| freMTPL2freq | 678,013 | Policy-level exposure and claim counts |
| freMTPL2sev | 26,639 | Individual claim amounts |
Data is downloaded automatically on first run via Hugging Face mirror. If that fails, the loader falls back to OpenML and then generates calibrated synthetic data.
Original source: Dutang & Charpentier, CASdatasets R package.
| Layer | Tools |
|---|---|
| Data | pandas, numpy, scikit-learn |
| Statistics | scipy (GPD, KS test), statsmodels |
| Visualization | matplotlib, seaborn |
| Optimization | scipy.optimize (differential_evolution) |
| Deploy | Streamlit |
- Peaks Over Threshold (POT) — selecting threshold, fitting GPD via MLE, goodness-of-fit
- Hill estimator — tail index estimation, confirming heavy-tail behavior
- VaR and TVaR — analytical formulas from GPD parameters
- Return period analysis — communicating extreme loss in reinsurance language
- Quota Share vs XL — proportional vs non-proportional reinsurance mechanics
- Burning cost pricing — per-occurrence XL premium calculation
- Aggregate Stop Loss — protecting annual aggregate losses directly
- Monte Carlo simulation — building annual aggregate distribution from individual severities
- Differential evolution — global optimization for treaty structure
- Efficient frontier — risk vs cost trade-off visualization
- Stress testing — 5 standard adverse scenarios for P&C reinsurance
Arthur Motta — Statistics and Actuarial Science, UFRJ
GitHub | LinkedIn