Reinsurance Recovery

Study guide: Exam 5

Reinsurance Recovery is the amount an insurer expects to collect from its reinsurers on ceded losses and LAE. It is an asset — a receivable — not a reduction of the underlying liability, and the cedant remains liable to its policyholders whether or not the reinsurer pays.

$\text{Net Unpaid} = \text{Gross Unpaid} - \text{Ceded Unpaid}$

$\text{Ceded Ultimate} = \text{Ceded Reported} \times \text{CDF}^{\text{ceded}}$

Estimate gross and ceded separately and derive net as the difference. The ceded pattern is not the gross pattern: excess cessions attach only to large claims, so the ceded triangle develops later, more steeply and far more erratically than gross. See Reinsurance.
Ceded triangles are thin and volatile by construction — a handful of claims — so they are often estimated by applying the treaty terms to projected large-claim experience rather than by developing the ceded triangle directly.
Historical ceded data reflects the treaties as they then stood. A change in attachment point, limit or structure makes prior ceded years non-comparable, which is the reason net triangles are unreliable in a book whose reinsurance programme moves.
Collectability must be assessed: disputes over coverage, commutations that settle the recoverable for a lump sum, and reinsurer insolvency all reduce what actually arrives. Statutory reporting requires provisions for uncollectible reinsurance, and the actuary should state whether the estimate is before or after such a provision.
Ceded recoveries also lag in timing even when uncontested — the cedant pays the claim first and bills afterwards — so the cash-flow profile of a net position differs from its accounting profile.

Gross, Ceded and Net Ultimates AY 2023: gross reported losses $\$4{,}000{,}000$ with a gross CDF of $1.20$ ; ceded reported losses $\$900{,}000$ with a ceded CDF of $1.55$ under a per-occurrence excess treaty.

Compute the net ultimate, and compare with developing net losses directly at the gross factor.
Answer
 $\begin{align*} \text{Gross ultimate} &= \$4{,}000{,}000 \times 1.20 = \$4{,}800{,}000 \\[4pt] \text{Ceded ultimate} &= \$900{,}000 \times 1.55 = \$1{,}395{,}000 \\[4pt] \text{Net ultimate} &= \$4{,}800{,}000 - \$1{,}395{,}000 \\ &= \$3{,}405{,}000 \end{align*}$ 
Developing net losses directly at the gross factor instead:

$(\$4{,}000{,}000 - \$900{,}000) \times 1.20 = \$3{,}720{,}000$

a difference of $\$315{,}000$ , or $9\%$ of the net reserve. The shortcut assumes ceded losses develop at the same rate as gross, which under an excess treaty they emphatically do not — the large claims that pierce the retention are still maturing into the layer.

The direction of the error is systematic, not random: netting first and developing at the gross factor always overstates net losses when the ceded layer is longer-tailed than gross.

A Change in Treaty Structure An insurer's per-occurrence retention history: $\$250{,}000$ through $2021$ , raised to $\$1{,}000{,}000$ from $1/1/2022$ . Ceded losses as a percentage of gross, by accident year at $36$ months: $2019$ $22\%$ , $2020$ $24\%$ , $2021$ $21\%$ , $2022$ $9\%$ , $2023$ $8\%$ .

How should the ceded reserve for AY 2023 be estimated?

Answer The drop from $\approx 22\%$ to $\approx 8\%$ is the retention change, not a change in loss experience. The pre- $2022$ ceded history describes a treaty that no longer exists.

Not usable: ceded development factors from $2019$ – $2021$ , or any ratio-to-gross benchmark from those years.

Usable approaches:

Apply current treaty terms to projected claim severities. Project the gross large-claim distribution for AY 2023, apply $\min(\max(X - \$1\text{M},0),\, L)$ claim by claim, and sum. This is exposure rating and it is insensitive to the treaty history entirely.

Restate the historical ceded triangle to current terms — recompute what each historical claim would have ceded under a $\$1$ M retention — and develop the restated triangle. More work, and it requires claim-level data, but it recovers the use of the history.

Both avoid the trap of developing a ceded triangle that mixes two treaties, and both make clear why net triangles are the wrong structure here: the net pattern changed discontinuously on $1/1/2022$ and no factor selection can span that break.