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Reserving for Reinsurance

Estimating liabilities for claims incurred, the discipline behind reserve adequacy and balance sheet strength.

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Reserves are the reinsurer's estimate of unpaid liabilities for claims already incurred, including those incurred but not reported (IBNR). Reserve adequacy is a core input to rating-agency assessments of balance sheet strength.

Chain-ladder

The workhorse method develops cumulative claims \\(C_{i,j}\\) (accident year \\(i\\), development year \\(j\\)) using age-to-age development factors:

Development factor
$$\hat f_j=\frac{\sum_i C_{i,j+1}}{\sum_i C_{i,j}}$$
Ultimate claims are projected by chaining the development factors; the reserve is ultimate minus paid-to-date.

Bornhuetter-Ferguson

Blends the chain-ladder projection with an a-priori expected loss, more stable for immature or volatile years, and well suited to long-tail reinsurance:

Bornhuetter-Ferguson reserve
$$R=\text{Premium}\times \text{ELR}\times\big(1-\tfrac{1}{\text{CDF}}\big)$$
ELR is the expected loss ratio; CDF the cumulative development factor to ultimate.

Reserving discipline

Power Re favors prudent, well-documented reserves with regular back-testing of development. Consistent, slightly favorable reserve development is precisely the signal rating agencies reward, and adverse development the signal they punish.

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