Allocation of Claims Under Reinsurance

A hurricane hits. Three policies produce losses of $150,000, $600,000, and $1,200,000. The insurer has a 25% quota share, a per-risk XOL of $800K xs $200K, and a catastrophe treaty of $5Mxs$1M. How much does each party pay? Misallocating one claim distorts reserves by hundreds of thousands.

HIGH-FREQUENCY: Computing exact dollar allocations across multi-layer reinsurance programs is a core FAM question type.

For a "$L$ xs $M$" treaty, three scenarios for claim $X$:

• $X\le M$: Cedant pays $X$. Reinsurer pays 0.
• $M<X\le M+L$: Cedant pays $M$. Reinsurer pays $X-M$.
• $X>M+L$: Cedant pays $X-L$. Reinsurer pays $L$.

TRAP: When $X>M+L$, the excess above the layer falls back to the cedant, not the reinsurer. The reinsurer pays at most $L$, never the amount above the layer.

Common mistakes

• Using the XOL limit as the top of the layer. "$300K xs $150K" has top at $150K+300K=450K$, not $300K. For a $400K claim, reinsurer pays $400K-150K=250K$, not $150K.
• Forgetting to apply QS before XOL when specified. If the problem states XOL applies to net retained loss after QS, you must reduce the loss first. Applying XOL to gross overstates the reinsurer's payment.
• Double-counting the QS cession. QS reinsurer pays $c\times X$ on gross. XOL reinsurer pays on net $(1-c)X$. Do not also apply $(1-c)$ to the XOL recovery.

Bottom line

• Per-risk XOL has three cases: below retention (cedant pays all), within layer (reinsurer pays excess over retention), above layer (reinsurer pays full limit, excess falls to cedant).
• Top of the layer is $M+L$, the retention plus the limit, not the limit alone. A $400K claim under 300K xs 150K recovers $250K.
• Layers stack lowest to highest: Layer 1 fills first, then Layer 2. Any excess above the top layer, including gaps between layers, returns to the cedant.
• Order matters: QS before XOL shrinks the loss before the layer tests it; XOL before QS applies to gross. QS reinsurer pays $c\times X$, XOL pays on net $(1-c)X$.

Exam shortcut

For multi-treaty problems, set up a table: Gross Loss, QS Reinsurer, XOL Reinsurer, Cedant. Work through each treaty in order. Sum each row to verify. The 30 seconds spent on the table saves minutes of debugging. "Every dollar has a home." Sum all parties' shares. If the sum does not equal gross loss, there is an error.

The full lesson (about 1,831 words, 12 min read) adds 3 worked examples, all 5 common mistakes, a self-check, free in the app.

Learning objectives

• 1e

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