Types of Reinsurance

Study guides: Exam DISC-RM, Exam 6C, Exam 7, Exam 9, Exam CP-341

Types of Reinsurance are classified on two independent axes: how the cover is placed — treaty (a whole portfolio, ceded automatically) or facultative (one risk, underwritten on its own) — and how losses are shared — proportional (the reinsurer takes the same share of premium and of loss) or non-proportional (the reinsurer pays only the part of a loss above a retention).

$\text{Ceded}_{\text{QS}} = a\,X$

$\text{Ceded}_{\text{SS}} = \frac{\min\left(\max(V - R,\,0),\; N R\right)}{V}\,X$

$\text{Ceded}_{\text{XS}} = \min\left(\max(X - R,\,0),\; L\right)$

$\text{Ceded}_{\text{Agg}} = \min\left(\max(S - A,\,0),\; L_A\right)$

$X$ is one loss (on a risk, a policy or an occurrence); $a$ the quota share cession; $V$ the risk's insured value; $R$ the retention (the retained line for surplus share); $N$ the number of lines; $L$ the layer limit; $S$ the aggregate loss for the period; $A$ and $L_A$ the aggregate retention and limit.
Proportional: Quota Share (the same percentage of every policy) and Surplus Share (a percentage that rises with the risk's size), each with a ceding commission for the cedant's expenses. Non-proportional: Excess of Loss per risk, per occurrence (casualty, including high clash layers, and property catastrophe), and Aggregate Excess of Loss (stop loss, or an aggregate deductible on a layer).
The two axes cross. A treaty can be quota share, surplus share or excess; a facultative certificate can be pro rata or excess. Order matters too: a surplus share may inure to the benefit of a per-risk or catastrophe cover, which then applies to what the cedant has left after it.
Function (Exam 7). Capacity to write larger risks than surplus supports; stabilisation of results; catastrophe protection; surplus relief, since a proportional cession's ceding commission recovers acquisition cost on the unearned premium; access to the reinsurer's underwriting expertise; and a way out of a line.
Loss cost (Exam 9). Proportional contracts are priced as a loss ratio on ceded premium; excess contracts as a loss cost on subject premium, from experience and exposure rating; aggregate contracts need the full aggregate loss distribution. Reinsurance Contract Provisions then change the result — see Reinsurance Pricing.
Statements and reserves (Exams 6C, 7). Proportional cessions scale with gross and develop like it. Excess cessions carry little premium but sit on large, late-reported claims, so actuaries typically select development patterns and expected loss ratios gross and net of reinsurance and take ceded as the difference (Reinsurance Reserving). In Canada, under IFRS 17, every type is a reinsurance contract held, recognized and presented separately from the underlying contracts rather than netted against gross. A commission that does not depend on claims reduces the premium paid; one contingent on claims (a sliding scale or profit commission) is treated as part of the claims expected to be recovered. MCT credit depends on registered or unregistered status. A structure that fails Risk Transfer is deposit-accounted.

One Fire Loss Under Three Treaty Types A commercial property with insured value $\$2{,}000{,}000$ suffers a fire. Compute the ceded amount for a loss of (i) $\$600{,}000$ and (ii) $\$100{,}000$ under each of: (a) a $30\%$ quota share; (b) a surplus share with a $\$250{,}000$ line and $6$ lines; (c) a $\$750{,}000$ xs $\$250{,}000$ per-risk excess.
Answer Surplus share cession for this risk (capacity $6 \times \$250\text{K} = \$1{,}500\text{K}$ ):
 $\begin{align*} s &= \frac{\min(2{,}000 - 250,\ 1{,}500)}{2{,}000} \\ &= \frac{1{,}500}{2{,}000} \\ &= 75\% \end{align*}$ 
(i) Loss of $\$600{,}000$ :

Quota share: $0.30 \times \$600\text{K} = \$180\text{K}$ .

Surplus share: $0.75 \times \$600\text{K} = \$450\text{K}$ . The cedant keeps $25\%$ — its $12.5\%$ line plus the $12.5\%$ of value above the treaty's capacity, unless it buys facultative cover for that top slice.

Excess: $\min(\max(600 - 250, 0), 750) = \$350\text{K}$ .

(ii) Loss of $\$100{,}000$ :

Quota share: $\$30\text{K}$ .

Surplus share: $0.75 \times \$100\text{K} = \$75\text{K}$ .

Excess: $\$0$ , since the loss is below the retention.

The small loss is the telling case: surplus share is not excess insurance. Once the risk's share is fixed by its size, the reinsurer pays that share of every loss on it, however small. Only the excess treaty cedes nothing below $\$250{,}000$ .

Matching the Type to the Need Recommend a type of reinsurance for each cedant: (1) a fast-growing regional insurer whose premium-to-surplus ratio is above its target; (2) a commercial property writer with a few very large buildings in a book of small ones; (3) a coastal homeowners writer whose modelled 1-in-250 hurricane loss exceeds its risk tolerance; (4) a writer worried about a year of many medium-sized losses, none large enough to reach a per-risk layer; (5) an insurer asked to write one unusual chemical plant that its treaties exclude.

Answer

Quota share. It cedes premium and unearned premium, and the ceding commission recovers the acquisition cost already paid, so net premium falls and surplus rises: surplus relief and capacity.

Surplus share (or a per-risk excess). The surplus share cedes a large percentage of the large risks and none of the small ones, which evens out the net amount at risk per building.

Catastrophe excess of loss per occurrence, sized to the modelled loss, with Reinstatements so a second event is also covered.

Aggregate excess of loss (stop loss), which responds to the year's total. The attachment must be reachable, or the contract fails risk transfer.

Facultative, pro rata or excess, underwritten by the reinsurer on that plant alone.