Reinsurance Pricing Methods

Following the CAS/SOA framework (Clark, Basics of Reinsurance Pricing), a reinsurance layer is priced with three complementary lenses.

1. Burning cost

The simplest experience-based method: historical losses to the layer, divided by exposure (often premium), trended and developed.

Burning cost

$$\text{Burning Cost}=\frac{\sum \text{losses to the layer}}{\sum \text{exposure}}$$

Losses are indexed for inflation and developed to ultimate; exposure is on-levelled.

2. Experience rating

Uses the cedant's own historical losses, capped and developed to the layer, to estimate the expected loss cost. Reliable when the data are credible and representative; weak for high, rarely-penetrated layers.

Expected layer loss (experience)

$$E[L]=\lambda\,E\big[\min(\max(X-d,0),\ell)\big]$$

lambda is the expected claim frequency to the layer; the expectation is the average severity in the layer l xs d.

3. Exposure rating

Uses industry exposure curves or increased limits factors (ILFs) to allocate the expected loss to the layer, independent of the cedant's own experience. Essential when experience is thin or the layer is high. See exposure curves.

Credibility blend

Best practice blends experience and exposure estimates by credibility \$Z\$:

Credibility-weighted price

$$\widehat{E[L]}=Z\cdot E[L]_{\text{exp}}+(1-Z)\cdot E[L]_{\text{expo}}$$

Z rises with the volume and stability of the cedant own experience. See Credibility Theory.

From loss cost to premium

The technical premium loads the expected loss for expenses, cost of capital and profit, and for the risk (volatility) of the layer, often via a standard-deviation or a risk-adjusted (utility / distortion) principle.