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 just 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, and cession percentages—appear frequently in both multiple choice and free-response questions.

Think of reinsurance structures as tools in a risk management toolkit. Each one 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 reinsurance 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

• Fixed cession percentage applies to all policies—if an insurer cedes 40%, the reinsurer receives 40% of premiums and pays 40% of all losses regardless of size
• Simplifies administration and capital management because the ratio remains constant across the entire portfolio
• Ceding commission offsets the insurer's acquisition costs, making this structure attractive for new or growing books of business

Surplus Reinsurance

• Variable cession based on policy size—the insurer retains up to a set limit (the "line"), ceding only the surplus above that amount
• Retention formula: if retention is $R$ and policy limit is $L$, cession percentage equals $\frac{L - R}{L}$ when $L > R$
• Preserves premium on smaller risks while transferring exposure on larger policies, giving insurers 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)

• Attachment point defines where coverage begins—the insurer retains losses up to threshold $A$, and the reinsurer covers losses between $A$ and the limit $A + L$
• Per-risk vs. per-occurrence basis determines whether the attachment applies to individual claims or aggregate event losses
• Loss calculation: reinsurer pays $\min(X - A, L)$ when loss $X > A$, where $L$ is the layer limit

Stop Loss Reinsurance (Aggregate XOL)

• Covers total losses exceeding a threshold over a defined period—typically expressed as a percentage of expected losses or earned premium
• Aggregate attachment point protects against accumulation of moderate losses rather than single large events
• Smooths underwriting results by capping the insurer's annual loss ratio, essential for financial planning

Catastrophe Reinsurance

• High attachment points designed for extreme events—covers losses from a single catastrophic occurrence affecting multiple policies
• Reinstatement provisions specify how coverage is restored after a loss and at what additional premium
• Essential for solvency protection in regions exposed to hurricanes, earthquakes, or other correlated perils

---

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

• Automatic coverage for defined classes of business—once negotiated, all qualifying risks are ceded without individual approval
• Reduces transaction costs and provides predictable capacity for the insurer's ongoing operations
• Obligatory for both parties: the reinsurer must accept risks meeting treaty terms, and the insurer must cede them

Facultative Reinsurance

• Individual risk evaluation and acceptance—each policy is separately underwritten by the reinsurer
• Used for risks outside treaty parameters: unusually large exposures, unique hazards, or classes not covered by existing agreements
• Higher administrative burden but provides flexibility for non-standard situations

---

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

• Limited risk transfer with profit-sharing features—the reinsurer's maximum exposure is capped, and experience accounts track cumulative results
• Spreads losses over time rather than transferring them entirely, blending insurance and financing elements
• Loss corridors and sliding scale commissions align incentives and share favorable or adverse experience between parties

---

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.