Key Reinsurance Structures

Why This Matters

Reinsurance sits at the heart of actuarial risk management. It's the mechanism that allows insurers to write policies they couldn't otherwise afford to hold. On your exam, you're being tested on more than definitions; you need to understand how risk transfers between parties, when premium and loss sharing occurs, and why certain structures suit specific risk profiles. The mathematical relationships underlying these structures (retention limits, attachment points, cession percentages) appear frequently in both multiple choice and free-response questions.

Each reinsurance structure solves a different problem: smoothing earnings volatility, protecting against catastrophic losses, or managing capital requirements. Don't just memorize the names. Know what problem each structure solves, how the cash flows work, and when an actuary would recommend one over another. The exam loves to test your ability to match a scenario to the appropriate structure.

---

Proportional Structures: Sharing Risk from Dollar One

Proportional reinsurance divides premiums and losses between the insurer and reinsurer according to predetermined percentages. The key principle: both parties share in every dollar of premium and every dollar of loss, creating aligned incentives throughout the policy period.

Quota Share Reinsurance

A fixed cession percentage applies uniformly to all policies in the covered book. If an insurer cedes 40%, the reinsurer receives 40% of premiums and pays 40% of all losses, regardless of claim size.

This simplicity makes quota share easy to administer and particularly useful for capital management. A growing insurer that needs to free up surplus to support new business will often turn to quota share first. The reinsurer typically pays a ceding commission back to the insurer to offset acquisition costs (agent commissions, underwriting expenses), which makes the arrangement financially viable even though the insurer is giving up a large share of premium.

Surplus Reinsurance

Surplus reinsurance uses a variable cession percentage that depends on each policy's size. The insurer sets a retention amount (called a "line"), and only the portion of each policy's limit that exceeds that line gets ceded.

The cession percentage for a given policy is:

$\frac{L - R}{L} \quad \text{when } L > R$

where $R$ is the insurer's retention (line) and $L$ is the policy limit. If $L \leq R$, nothing is ceded.

For example, suppose the insurer's line is $\$500{,}000$. On a policy with a $\$2{,}000{,}000$ limit, the cession percentage is $\frac{2{,}000{,}000 - 500{,}000}{2{,}000{,}000} = 75\%$. But on a $\$400{,}000$ policy, the insurer retains 100%. This structure preserves premium on smaller risks while transferring exposure on larger ones, giving the insurer more control over portfolio composition.

---

Non-Proportional Structures: Protection Above a Threshold

Non-proportional reinsurance activates only when losses exceed specified triggers. The insurer pays a fixed premium for coverage that may never be used, similar to buying high-deductible insurance. These structures protect against severity rather than sharing in frequency.

Excess of Loss Reinsurance (XOL)

XOL coverage begins at an attachment point $A$. The insurer retains all losses up to $A$, and the reinsurer covers losses in the layer between $A$ and $A + L$, where $L$ is the layer limit. The reinsurer's payment on a loss of size $X$ is:

$\text{Reinsurer pays} = \min(X - A,\; L) \quad \text{when } X > A$

If $X \leq A$, the reinsurer pays nothing.

A critical distinction is the basis of the attachment:

• Per-risk XOL: the attachment point applies to each individual claim separately. Useful when the insurer is concerned about a single large loss on one policy.
• Per-occurrence XOL: the attachment point applies to the total losses from a single event across all affected policies. This is the basis used for catastrophe reinsurance (discussed below).

Stop Loss Reinsurance (Aggregate XOL)

Stop loss reinsurance covers total accumulated losses over a defined period (usually one year) once they exceed an aggregate threshold. That threshold is typically expressed as a percentage of earned premium or expected losses.

For instance, a stop loss contract might attach at 80% of earned premium. If the insurer's aggregate losses stay below that ratio, the reinsurer pays nothing. If losses reach 95% of earned premium, the reinsurer covers the excess above 80% (subject to a cap).

This structure protects against an accumulation of moderate losses rather than a single large event. It smooths underwriting results by capping the insurer's annual loss ratio, which is valuable for financial planning and earnings stability.

Catastrophe Reinsurance

Catastrophe reinsurance is a specific application of per-occurrence XOL with very high attachment points designed for extreme events like hurricanes, earthquakes, or wildfires that affect many policies simultaneously.

Two features distinguish catastrophe covers from standard XOL:

• Reinstatement provisions specify how coverage is restored after a loss event triggers the layer. The insurer typically pays an additional reinstatement premium (often pro rata to the proportion of the layer exhausted) to restore the full limit for subsequent events.
• Hours clauses define the time window within which individual losses are grouped into a single occurrence (commonly 72 to 168 hours for windstorm events).

Catastrophe reinsurance is essential for solvency protection in regions exposed to correlated perils, where a single event can generate losses many multiples of a normal year.

---

Agreement Types: How Contracts Are Structured

Beyond the risk-sharing mechanism, reinsurance contracts differ in how risks are selected and bound. This distinction affects pricing, administration, and the insurer's flexibility.

Treaty Reinsurance

Treaty reinsurance provides automatic coverage for defined classes of business. Once the treaty is negotiated, all qualifying risks are ceded without individual approval from the reinsurer.

The arrangement is obligatory for both parties: the reinsurer must accept all risks meeting the treaty terms, and the insurer must cede them. This reduces transaction costs and provides predictable capacity for the insurer's ongoing operations. Most quota share and surplus arrangements are structured as treaties.

Facultative Reinsurance

Facultative reinsurance involves individual risk evaluation and acceptance. Each policy is separately submitted to and underwritten by the reinsurer, who can accept or decline.

This approach is used for risks that fall outside treaty parameters: unusually large exposures, unique hazards, or classes not covered by existing agreements. The administrative burden is higher, but it provides flexibility for non-standard situations where treaty terms don't apply.

---

Hybrid and Specialized Structures

Some reinsurance arrangements blend features of multiple structures or address specific long-term objectives beyond simple risk transfer.

Finite Risk Reinsurance

Finite risk reinsurance involves limited risk transfer combined with profit-sharing features. The reinsurer's maximum exposure is capped, and an experience account tracks cumulative premiums, investment income, and losses over the contract's multi-year term.

The structure spreads losses over time rather than transferring them entirely, blending insurance and financing elements. Common features include:

• Loss corridors where the insurer retains a band of losses within the reinsured layer
• Sliding scale commissions that adjust based on actual loss experience, rewarding favorable results and sharing adverse outcomes

Because the risk transfer component can be relatively small compared to the financing component, regulators scrutinize finite deals carefully. If the arrangement doesn't transfer sufficient underwriting risk (both in timing and amount), it may not qualify as reinsurance for statutory accounting purposes and must instead be treated as a deposit or loan.

---

Quick Reference Table

---

Self-Check Questions

1. An insurer wants to cede a fixed percentage of every policy in its auto book. Which structure applies, and how would the reinsurer's loss payment be calculated if the cession rate is 30% and a claim is $\$50{,}000$?

2. Compare surplus reinsurance and quota share: what key factor determines the cession percentage in each, and which gives the insurer more premium retention on small policies?

3. A property insurer faces hurricane exposure and wants protection only if a single storm causes losses exceeding $\$10$ million. Which structure is most appropriate, and what is the technical term for the $\$10$ million threshold?

4. When would an insurer use facultative reinsurance instead of relying on an existing treaty? Give two specific scenarios.

5. An FRQ describes a reinsurance contract with a profit-sharing account, loss corridors, and a cap on the reinsurer's total payout. Identify the structure and explain why regulators might question whether it qualifies as true risk transfer.