Ceded Loss Reserve

Study guide: Exam 7

Ceded loss reserves are the part of an insurer's unpaid claims (case reserves plus IBNR, and loss adjustment expense where the treaty covers it) expected to be recovered from reinsurers under the contracts in force. From the cedant's side they are the unpaid portion of ceded losses, carried as a reinsurance recoverable asset.

\text{Ceded unpaid} = \text{Gross unpaid} - \text{Net unpaid}

\text{Ceded IBNR} = \text{Ceded ultimate} - \text{Ceded reported}

• By treaty type (see Types of Reinsurance):
  • Quota share cedes a fixed percentage of ultimate, paid, case and IBNR alike. When the percentage changes, it follows the policy year on a risks-attaching treaty and the accident year on a losses-occurring-during treaty.
  • Surplus share varies the cession by risk.
  • Per-risk or per-occurrence excess of loss applies \min(\max(X - R, 0), L) to projected ultimates of large claims. Alternatively, develop a ceded triangle, or run BF with a ceded expected loss ratio.
  • Stop-loss and aggregate covers cap the retained total.
• Order matters. Covers inure in a stated sequence. Typically per-occurrence excess comes off first, then the quota share applies to what remains, and the stop-loss applies last to protect the final net result.
• Estimate two, derive the third. Friedland describes two approaches: project gross and net and take ceded as the difference, or project gross and ceded and take net as the difference. Actuaries typically use the first, selecting development patterns and expected loss ratios gross and net. Ceded data often have limited credibility: a lower volume of losses, volatility from large claims and catastrophes, and frequent changes in attachment points, limits, participation and ALAE treatment. Then check:
  • ceded is non-negative and net never exceeds gross;
  • on excess of loss cessions, ceded IBNR is a larger share of ceded ultimate than gross IBNR is of gross, because excess cessions develop late;
  • on excess of loss cessions, implied ceded development factors exceed gross ones. On a quota share the gross, ceded and net factors are identical.
• Why ceded data is harder. Trend is leveraged into excess layers, reporting thresholds delay notice, and a change in retention makes prior ceded years non-comparable. The treaty history must be kept alongside the data.
• It is an asset with credit risk. Recoverables can be disputed, commuted (Commutations) or lost to a reinsurer's insolvency (Reinsurance Credit Risk), and the cedant stays liable to its policyholders. See Reinsurance Recovery and, for the reinsurer's side of the same liability, Reinsurance Reserving.

Inuring Order Across Three Covers For one accident year the gross ultimate is 5{,}000 and gross paid is 3{,}000 ($000s). One large claim has an ultimate of 600 and paid of 100. The cedant has three covers, inuring in this order:

1. a per-occurrence excess of 400 xs 200;
2. a 30\% quota share;
3. a stop-loss capping retained losses after the quota share at 3{,}000.

Compute the ceded unpaid by cover and the net unpaid.

Answer Excess of loss, on the large claim:

\begin{align*}
\text{Ceded ult} &= \min(600 - 200,\ 400) \\
&= 400 \\
\text{Ceded paid} &= \max(100 - 200,\ 0) \\
&= 0
\end{align*}

The remainder is an ultimate of 4{,}600 and paid of 3{,}000.

Quota share at 30\% cedes an ultimate of 1{,}380 and paid of 900, so its ceded unpaid is 480. That leaves a retained ultimate of 3{,}220 and paid of 2{,}100.

Stop-loss: the ceded ultimate is 3{,}220 - 3{,}000 = 220, and nothing is ceded on paid because 2{,}100 < 3{,}000. Its ceded unpaid is 220.

\begin{align*}
\text{Ceded unpaid} &= 400 + 480 + 220 \\
&= 1{,}100 \\
\text{Net unpaid} &= 3{,}000 - 2{,}100 \\
&= 900
\end{align*}

Check: gross unpaid 2{,}000 = 1{,}100 + 900. ✓ Applying the quota share before the excess cover would have ceded 30\% of the large claim to the quota share and changed every figure. The treaty wording on inuring decides which is right.

An Inconsistent Net Estimate A cedant with a \$1M xs \$500K per-risk treaty estimates gross and net separately by chain ladder ($000s):

AY	Gross ult	Gross rep	Net ult	Net rep
2023	10{,}000	7{,}000	8{,}600	6{,}200
2024	11{,}000	5{,}000	10{,}300	4{,}300

Are the implied ceded reserves reasonable?

Answer

\begin{align*}
\text{Ceded IBNR}_{2023} &= (10{,}000 - 8{,}600) - (7{,}000 - 6{,}200) \\
&= 600 \\
\text{Ceded IBNR}_{2024} &= (11{,}000 - 10{,}300) - (5{,}000 - 4{,}300) \\
&= 0
\end{align*}

For 2024, the whole gross IBNR of 6{,}000 is retained, and the ceded ultimate equals what has already been ceded. For an excess treaty at 12 months that is implausible. Claims pierce the retention late, so ceded IBNR should be the largest part of ceded ultimate for the youngest year. The net chain ladder has applied net factors to a diagonal with too few large claims yet.

Ceded is still the difference between gross and net; the net projection for 2024 is what needs replacing. A method that leans less on the thin diagonal, such as the expected claims method with a net expected loss ratio consistent with the gross one and the treaty terms, fixes it. If pricing or exposure rating expects 12\% of gross ultimate to be ceded, net ultimate is 11{,}000 \times 0.88 = 9{,}680. Ceded ultimate is then 1{,}320 and ceded IBNR 620, with net 620 below the net chain ladder.