Insurance calculators
Reinsurance structures
Apply surplus, quota share, per-risk excess of loss and aggregate stop loss treaties to a list of losses and see gross, ceded and net amounts.
Inputs
Results
Gross losses
4,130,000.00
Ceded
3,235,000.00
78.3%
Net retained
895,000.00
By loss
| Loss | Gross | Surplus | Quota share | XoL | Net |
|---|---|---|---|---|---|
| 1 | 450,000.00 | 225,000.00 | 0.00 | 0.00 | 225,000.00 |
| 2 | 120,000.00 | 0.00 | 0.00 | 0.00 | 120,000.00 |
| 3 | 2,600,000.00 | 2,080,000.00 | 0.00 | 270,000.00 | 250,000.00 |
| 4 | 60,000.00 | 10,000.00 | 0.00 | 0.00 | 50,000.00 |
| 5 | 900,000.00 | 642,857.14 | 0.00 | 7,142.86 | 250,000.00 |
| Total | 4,130,000.00 | 2,957,857.14 | 0.00 | 277,142.86 | 895,000.00 |
Methodology
Conventions
- The treaties apply in this order: surplus on the sums insured, then quota share on what is retained, then per-risk excess of loss on each retained loss, then an aggregate stop loss on the year's retained total.
- Surplus cedes the share of each risk above the retention line, up to the number of lines, and applies the same share to the loss.
References
- Swiss Re, An introduction to reinsurance.
- Klugman, Panjer and Willmot, Loss Models: From Data to Decisions, 5th ed.
Formulas
- Surplus share
- s = \min\big(\max(SI - R, 0),\, nR\big) / SI
- Quota share
- \text{ceded} = q \times \text{loss}
- Excess of loss
- \text{ceded} = \min\big(\max(X - R, 0), L\big)
- Stop loss
- \text{ceded} = \min\big(\max(S - A, 0), L\big)