Reinsurance Decision Lab

Harbour Mutual expects 40 claims per year. Ground-up severity is modelled as lognormal with mean about £5,000 and log-scale SD 1. Compare:

• No treaty;
• 40% quota share: insurer retains 60% of each covered loss;
• £20,000 xs £20,000 per loss: ceded $=\min\{(X-20{,}000)_+,20{,}000\}$.

This is a loss-only comparison: premium, commission, reinstatement, expenses, counterparty default, and dependence are excluded.

1. Check three claims by hand

The XL layer targets medium-large claims but exposes the insurer again above £40,000.

2. Simulate annual outcomes

Monte Carlo output varies slightly. The comparison is reproducible because the seed, sample size, distribution, and treaty functions are visible.

3. Interpret, do not rank mechanically

The lowest net VaR is not automatically the best treaty. Compare net underwriting result after reinsurance price and consider liquidity, counterparty, basis, and strategic constraints.

4. Validate the simulation

For compound Poisson gross loss with independent severity,

Also,

Simulation mean and SD should be close to analytical values within Monte Carlo error. If not, inspect parameterisation and units before interpreting tail results.

5. Extend one assumption at a time

Try these in the cell:

1. multiply each severity by 1.10 while keeping layer terms fixed;
2. increase log-scale $\sigma$ from 1.0 to 1.3 while preserving mean;
3. add an annual catastrophe state that increases count and severity together;
4. change the treaty to £50,000 xs £10,000;
5. add a second reinstatement-limited occurrence layer only after defining events.

For each change, predict direction before running. Then explain whether mean, SD, attachment, exhaustion, VaR, or TVaR moved most.

6. Decision memo template

Conclude in six lines:

1. portfolio and valuation basis;
2. treaties and precise loss functions;
3. gross versus net mean and tail metrics;
4. price/commission assumptions;
5. key sensitivity and data limitation;
6. recommendation and condition that would reverse it.

Next, connect the transformed losses to aggregate risk models.