Per-Claim Versus Per-Occurrence Limits

Why the Limit Basis Matters

A single accident can produce claims from several injured people or for several damaged properties. A policy limit may cap the insurer's payment separately for each claim, or cap the combined payment for all claims arising from one occurrence. Those are different contracts: even when the individual claim amounts and the stated limit are identical, the total insurer payment can differ substantially.

The calculation depends first on identifying which claims belong to the same occurrence and then applying the limit at the level specified by the policy. The examples below consider hypothetical policies and events. Unless stated otherwise, amounts are in thousands of dollars, there is no deductible, and there is no annual aggregate limit or other coverage adjustment.

Definition: A per-claim limit $u$ is the maximum insurer payment for each covered claim. A per-occurrence limit $u$ is the maximum combined insurer payment for all covered claims arising from one occurrence. For claim losses $x_1,\ldots,x_n$ from one occurrence, with nonnegative amounts and no deductible, the total payments are $$ I_{\text{claim}}=\sum_{j=1}^{n}\min(x_j,u) \qquad\text{and}\qquad I_{\text{occ}}=\min\left(\sum_{j=1}^{n}x_j,u\right). $$

The subscript identifies where the cap is applied. Under the per-claim basis, compare each claim separately with $u$, cap each one, and then add the capped amounts. Under the per-occurrence basis, add the losses from the occurrence first and cap that total once. A claim below the limit is not automatically paid in full if other policy terms apply; the formulas isolate the limit effect by assuming all claims are covered and that no other terms reduce payment.

Calculating the Two Limit Bases

A reliable calculation keeps the claim amounts visible until the correct cap has been applied. In particular, do not combine claims before applying a per-claim limit, and do not give every claim a separate limit when the contract provides one per occurrence.

Worked Example: One Event, Three Claims, and a Binding Cap

A hypothetical warehouse delivery accident produces three covered property claims of $180$, $120$, and $40$ thousand dollars. The policy limit is $u=200$ thousand dollars. Calculate total insurer payment under a per-claim limit and under a per-occurrence limit.

Method: apply the cap at the level named in the policy. Under the per-claim limit, cap each loss separately:

\min(180,200)=180,\qquad \min(120,200)=120,\qquad \min(40,200)=40.

The total per-claim payment is $180+120+40=340$ thousand dollars. None of the three claims individually exceeds the limit.

Under the per-occurrence limit, first add the three losses: $180+120+40=340$ thousand dollars. Then apply the single occurrence cap: $\min(340,200)=200$ thousand dollars.

Check. The per-claim payment is $340$ thousand dollars, while the per-occurrence payment is $200$ thousand dollars. The common mistake is to apply the occurrence limit separately to all three claims, which would incorrectly produce $340$ thousand dollars.

Why Per-Claim Payment Cannot Be Lower

For nonnegative claim amounts and the same limit $u$, the per-claim total is at least as large as the per-occurrence total. To see why, let $S=\sum_{j=1}^{n}x_j$. If $S\leq u$, every $x_j\leq u$, so neither basis reduces the total and both pay $S$. If $S>u$, the occurrence basis pays $u$. The sum of individually capped claims is at least $u$: if any claim is at least $u$, its capped amount alone is $u$; if none is at least $u$, no claim is capped and their sum is $S>u$. Thus,

\sum_{j=1}^{n}\min(x_j,u)\ \geq\ \min\left(\sum_{j=1}^{n}x_j,u\right).

The inequality can be an equality. For example, both bases pay the full loss total when the combined claims do not exceed $u$. If the combined losses exceed $u$, a per-claim basis can still pay more because separate claims can each use part, or all, of their own limit. This is why the limit basis matters most when multiple claims from the same event collectively exceed the stated limit.

Key result: With nonnegative losses and the same limit $u$, a per-claim limit never produces a lower total payment than a per-occurrence limit for claims from one occurrence. If the combined losses are at most $u$, both bases pay the same total. If the combined losses exceed $u$, the per-occurrence payment is $u$, while the per-claim payment may be greater.

Worked Example: Several Claims Below the Limit but Above It in Total

A hypothetical municipal maintenance incident causes claims of $90$, $70$, and $30$ thousand dollars. The stated limit is $u=250$ thousand dollars. Determine whether either limit basis reduces the total loss.

Method: compare the individual amounts and the combined amount with $u$. For a per-claim limit, each claim is below $250$, so the payments are $90$, $70$, and $30$ thousand dollars. Their sum is $90+70+30=190$ thousand dollars.

For a per-occurrence limit, first aggregate the claims: $90+70+30=190$ thousand dollars. The capped total is $\min(190,250)=190$ thousand dollars.

Check. Both bases pay $190$ thousand dollars because the combined losses are below the limit. The common mistake is to assume the two bases must always produce different totals merely because the wording differs; the wording changes the cap calculation, but it does not change a total that never reaches the cap.

Claims Must Be Grouped by Occurrence

A per-occurrence limit is applied separately to each occurrence, not once to every claim in the policy period. Therefore, identify the event grouping before summing losses. If two separate occurrences each generate claims, each occurrence receives its own cap under a per-occurrence limit, unless the contract also specifies an aggregate limit. The event definition and any policy-specific aggregation terms determine which claims belong together; the claim amounts alone do not establish that grouping.

Worked Example: Applying One Occurrence Limit to Each Event

A hypothetical contractor's policy has a per-occurrence limit of $180$ thousand dollars. During the period, one equipment failure gives rise to claims of $140$ and $90$ thousand dollars. A separate incident gives rise to claims of $210$ and $20$ thousand dollars. Assume the two incidents are distinct occurrences. Compare total payment under a per-occurrence limit with total payment under a per-claim limit of the same $180$ thousand dollars.

Method: preserve the event groups, then apply the relevant cap. For the per-occurrence basis, the first occurrence has losses $140+90=230$ thousand dollars, so its payment is $\min(230,180)=180$ thousand dollars. The second occurrence has losses $210+20=230$ thousand dollars, so its payment is also $\min(230,180)=180$ thousand dollars. Total per-occurrence payment is $180+180=360$ thousand dollars.

For the per-claim basis, apply the $180$ thousand dollar cap to each claim: $\min(140,180)=140$, $\min(90,180)=90$, $\min(210,180)=180$, and $\min(20,180)=20$. Total per-claim payment is $140+90+180+20=430$ thousand dollars.

Check. The per-claim total $430$ thousand dollars exceeds the per-occurrence total $360$ thousand dollars, consistent with the inequality above. A common mistake is to apply one $180$ thousand dollar cap to the entire policy period, yielding $180$ thousand dollars; that would be an annual aggregate cap, not the stated per-occurrence cap.

When a Deductible Is Also Specified

A deductible does not change the meaning of the limit basis, but the policy must specify how it applies. For illustration, suppose a deductible $d$ applies separately to each claim and is taken before the stated limit $u$. The amount subject to the limit for claim $j$ is then $(x_j-d)_+=\max(x_j-d,0)$. Under a per-claim limit, cap each resulting amount and add; under a per-occurrence limit, add those resulting amounts and apply one occurrence cap. This setup is an assumption, not a universal rule for every contract.

I_{\text{claim}}=\sum_{j=1}^{n}\min\big((x_j-d)_+,u\big), \qquad I_{\text{occ}}=\min\left(\sum_{j=1}^{n}(x_j-d)_+,u\right).

Worked Example: Deductible Applied Before Either Limit Basis

A hypothetical policy specifies a $20$ thousand dollar deductible separately for each claim, followed by a limit of $120$ thousand dollars. One event produces claims of $95$, $80$, and $60$ thousand dollars. Calculate the total payment under each limit basis.

Method: subtract the stated per-claim deductible first. The amounts after deductibles are $95-20=75$, $80-20=60$, and $60-20=40$ thousand dollars. Each is positive and below $120$.

Under the per-claim limit, the payments remain $75$, $60$, and $40$ thousand dollars. Their sum is $75+60+40=175$ thousand dollars. Under the per-occurrence limit, add the post-deductible amounts first: $75+60+40=175$. Then apply the occurrence cap: $\min(175,120)=120$ thousand dollars.

Check. The two totals are $175$ and $120$ thousand dollars. The common mistake is to subtract the deductible only once from the combined event loss. That would not follow the stated contract, which applies the deductible separately to each claim before the limit.

Exam and Practice Checks

The essential sequence is: determine the claim grouping, apply any stated deductible in its specified manner, apply the limit at the stated claim or occurrence level, and then total payments at the requested level. This distinction is aligned with the CAS Exam 5 (Basic Ratemaking and Estimated Claim Liabilities) syllabus. In rating work, changing from a per-claim to a per-occurrence cap can change expected payments, so the limit basis must match the policy wording and the loss experience being analyzed.

Do not confuse a claim with an occurrence. One occurrence can produce multiple claims.
Do not cap too early or too late. The per-claim basis caps before summing; the per-occurrence basis sums before capping.
Do not treat a per-occurrence limit as an annual aggregate. Apply it to each distinct occurrence unless another contract term says otherwise.
State assumptions. Deductibles, coverage eligibility, allocation among claimants, and aggregate caps can affect actual payment beyond the basic formulas.

Check Your Understanding

For each problem, assume all stated claims are covered, amounts are in thousands of dollars, and no policy term applies except the deductible or limit explicitly stated. Give the requested total payment.

An event produces claims of $72$ and $58$, with a limit of $100$. Find the payment under each limit basis. (Answer: per-claim $130$; per-occurrence $100$.)
One event produces claims of $160$, $40$, and $15$, with a limit of $120$. Find the payment under each basis. (Answer: per-claim $175$; per-occurrence $120$.)
An event produces claims of $35$, $45$, and $20$, with a limit of $150$. Find the payment under each basis and state why they agree or differ. (Answer: both pay $100$, because the combined losses are below the limit.)
Two distinct events produce claims of $60$ and $50$ for the first event, and $100$ and $15$ for the second. The limit is $90$ per claim or per occurrence, as applicable. Compare total payments. (Answer: per-claim $215$; per-occurrence $180$.)
A policy applies a $10$ deductible separately to each claim, then an $80$ limit. One event produces claims of $55$, $35$, and $25$. Find total payment under each limit basis. (Answer: per-claim $85$; per-occurrence $80$.)

What You'll Learn