Reconciling Gross, Ceded, and Retained Premiums

Why Premium Reconciliation Matters

An insurer can collect premium from policyholders and cede part of that premium to reinsurers. A proportional reinsurer may also pay the insurer a ceding commission. These are distinct amounts: the direct premium is the starting point, the ceded premium is transferred to the reinsurer, and the commission offsets some of the ceded cost. A clear reconciliation prevents a commission from being mistaken for additional premium retained through risk sharing.

The accounting convention matters. Some reports show net written premium as direct premium less ceded premium and show ceding commissions separately. Other calculations ask for the insurer’s net premium after the commission has reduced the reinsurance cost. This tutorial states which convention is being used each time. Unless a problem says otherwise, amounts below are hypothetical, relate to the same accounting period, and exclude taxes, fees, and investment income. No interest, mortality, or loss-distribution assumptions are needed.

Definition: Gross direct premium is premium charged for the insurer’s direct policies before reinsurance deductions. Ceded premium is the amount paid or credited to reinsurers for assuming reinsurance coverage. A ceding commission is an amount the reinsurer pays the insurer, commonly under a proportional arrangement. Under the after-commission convention used here, net premium after commission equals gross direct premium minus ceded premium plus ceding commission.

The Reconciliation

Let $G$ denote gross direct premium, $C$ the ceded reinsurance premium, and $K$ the ceding commission received by the insurer. Under the after-commission convention, the reconciliation is

\text{Net premium after commission}=G-C+K.

The signs follow the cash flows: ceded premium is a cost to the insurer, so it is subtracted; a ceding commission is received by the insurer, so it is added. If the commission is a stated proportion $r$ of ceded premium, and the contract specifies that basis, then $K=rC$. The commission must be calculated on the ceded premium to which the contract applies—not automatically on all direct premium.

For a proportional cession, the ceded premium is usually determined by applying the cession share to the premium base stated in the problem or contract. For a nonproportional cover, such as excess-of-loss reinsurance, the reinsurer’s premium is usually priced separately. It is not necessarily a percentage of direct premium or a fixed fraction of losses. If there is no stated commission on that cover, use no commission for it.

Set the scope and basis.
Identify the policies or portfolio included, and confirm that every amount is written or earned premium for the same period.

Find each ceded premium.
Apply each stated cession to its specified premium base. Keep separate cessions separate until their bases are clear.

Calculate commissions.
Apply each commission rate only to the ceded premium eligible for that commission, or use a stated commission amount.

Reconcile and check.
Subtract ceded premiums from gross direct premium, add commissions for the after-commission measure, and check the result against the component amounts.

Why the Formula Holds

The formula is a direct cash-flow reconciliation. Starting with $G$, the insurer transfers $C$ to reinsurers, leaving $G-C$ before commissions. The insurer then receives $K$, leaving $G-C+K$. Equivalently, define the net ceded cost after commission as $C-K$. Subtracting that cost from direct premium gives the same result:

$$ G-(C-K)=G-C+K. $$

This identity does not determine how a treaty prices its reinsurance or whether a commission applies. Those amounts must come from the stated contract terms. It only reconciles the amounts once they are known.

Worked Reconciliations

Worked Example: Quota Share With a Ceding Commission

A hypothetical insurer writes $240,000 of direct premium for a portfolio. It cedes 35% under a quota-share agreement. The reinsurer pays a ceding commission of 28% of the ceded premium. Find the ceded premium, commission, and net premium after commission. All figures are written premium for the same period; no other reinsurance, fees, interest, or mortality assumptions apply.

Method. Apply the quota-share percentage to the direct premium, calculate the commission on that ceded amount, and use the after-commission reconciliation.

Step 1: Ceded premium.

$$ C=0.35(240{,}000)=84{,}000. $$

Step 2: Ceding commission. The stated commission basis is ceded premium, so

$$ K=0.28(84{,}000)=23{,}520. $$

Step 3: Net premium after commission.

$$ G-C+K=240{,}000-84{,}000+23{,}520=179{,}520. $$

Check. The ceded premium net of commission is $84{,}000-23{,}520=60{,}480$. Subtracting that net ceded cost from the original premium gives $240{,}000-60{,}480=179{,}520$, as required.

Common mistake avoided. Applying 28% to the full $240,000 would give an incorrect commission of $67,200. The commission applies to the $84,000 ceded premium, not to all direct premium.

Worked Example: Two Cessions With Different Commission Rates

A hypothetical insurer has $180,000 of direct premium in Segment A and $120,000 in Segment B. In Segment A, 30% of the premium is ceded facultatively first; a quota-share treaty then cedes 20% of the remaining Segment A premium. The facultative cession earns a 10% commission, and the quota-share cessions earn a 25% commission. In Segment B, 20% is ceded to the quota-share treaty, also with a 25% commission. Find the total ceded premium, total commission, and net premium after commission. All figures are written premium for the same period.

Method. Follow the stated sequence in Segment A: calculate the facultative cession first, then apply the treaty percentage to the remaining premium. Calculate each commission on its corresponding ceded premium.

Step 1: Segment A facultative cession.

$$ 0.30(180{,}000)=54{,}000. $$

The Segment A premium remaining after that cession is

$$ 180{,}000-54{,}000=126{,}000. $$

Step 2: Segment A quota-share cession. The treaty applies to the remaining $126,000:

$$ 0.20(126{,}000)=25{,}200. $$

Thus Segment A total ceded premium is $54{,}000+25{,}200=79{,}200$.

Step 3: Segment B quota-share cession.

$$ 0.20(120{,}000)=24{,}000. $$

Step 4: Total ceded premium.

$$ C=54{,}000+25{,}200+24{,}000=103{,}200. $$

Step 5: Total commission. The facultative commission is $0.10(54{,}000)=5{,}400$. The quota-share commission is $0.25(25{,}200+24{,}000)=12{,}300$. Therefore,

$$ K=5{,}400+12{,}300=17{,}700. $$

Step 6: Net premium after commission. Gross direct premium is $180{,}000+120{,}000=300{,}000$, so

$$ G-C+K=300{,}000-103{,}200+17{,}700=214{,}500. $$

Check. The insurer retains $180{,}000-79{,}200=100{,}800$ of Segment A premium before commission and $120{,}000-24{,}000=96{,}000$ of Segment B premium before commission. Together these are $196,800. Adding the $17,700 commission gives $214,500.

Common mistake avoided. Applying the Segment A treaty share to the full $180,000 would ignore the stated prior facultative cession. The treaty base is the remaining $126,000.

Worked Example: Proportional Cession Plus Excess-of-Loss Premium

A hypothetical insurer writes $500,000 of direct premium. It cedes 20% of that premium under a quota-share treaty, which pays a 30% ceding commission on its ceded premium. The insurer also pays $42,000 for an excess-of-loss cover; the problem states that this cover has no ceding commission. Find the ceded premium, commission, and net premium after both reinsurance costs. All amounts are written premium for the same period.

Method. Calculate the proportional ceded premium and its commission. Treat the excess-of-loss premium as a separate reinsurance cost, not as another percentage of the direct premium.

Step 1: Quota-share ceded premium.

C_{\mathrm{QS}}=0.20(500{,}000)=100{,}000.

Step 2: Quota-share commission.

$$ K=0.30(100{,}000)=30{,}000. $$

Step 3: Total reinsurance premium cost before commission. Include the separately priced excess-of-loss premium:

C_{\mathrm{total}}=100{,}000+42{,}000=142{,}000.

Step 4: Net premium after commission.

$$ 500{,}000-142{,}000+30{,}000=388{,}000. $$

Check. The total reinsurance cost after commission is $142{,}000-30{,}000=112{,}000$. The insurer’s net amount is $500{,}000-112{,}000=388{,}000$.

Common mistake avoided. The $42,000 excess-of-loss premium is not calculated as a share of the $500,000 direct premium: it is already given as a separately priced amount. It also earns no commission because the problem expressly says so.

Accounting Conventions and Common Traps

Always label the amount being reported. Under a convention that reports net written premium before ceding commission, the calculation is $G-C$. If commissions are displayed separately, they remain a separate item rather than being added to that reported net written premium. Under the after-commission convention, the amount is $G-C+K$. Both presentations can be internally consistent; confusion arises when a calculation switches between them without saying so.

For example, if gross direct premium is $1,200,000, ceded premium is $240,000, and commission is $36,000, the before-commission net written premium is $1{,}200{,}000-240{,}000=\$960{,}000$. The after-commission amount is $960{,}000+36{,}000=\$996{,}000$. Reporting $996,000 as the before-commission figure, or adding the commission twice, mixes conventions.

Do not confuse ceded premium with retained premium. Ceded premium goes to the reinsurer. The proportional premium remaining with the insurer before commission is gross premium less proportional ceded premium.
Do not apply every cession to the same base. Use the stated sequence and eligibility rules. A treaty may apply to the balance after a prior cession.
Do not assume all ceded premium earns commission. Use a commission only when the terms state one, and use its specified calculation base.
Do not mix written and earned amounts. Reconcile gross written premium with ceded written premium, or gross earned premium with ceded earned premium, for the same period and scope.
Do not call a result “net” without defining it. State whether commissions have been included and whether separately priced reinsurance costs are included.

Key takeaway: State the premium basis and accounting convention first. Then reconcile gross direct premium, each ceded premium, and each commission separately. Under the after-commission convention, subtract reinsurance premiums and add commissions received.

Check Your Understanding

For each problem, state the relevant ceded premium and commission before giving the requested net amount. Unless noted otherwise, all premiums are written for the same period and the after-commission convention applies.

A hypothetical insurer writes $360,000 of direct premium, cedes 40% under quota share, and receives a commission equal to 25% of the ceded premium. Find the net premium after commission. (Answer: ceded premium $144,000; commission $36,000; net $252,000.)
A portfolio has two segments: $200,000 with a 15% cession and 20% commission on that cession, and $160,000 with a 30% cession and 25% commission on that cession. Find total ceded premium, total commission, and net premium after commission. (Answer: ceded premium $78,000; commission $18,000; net $300,000.)
An insurer writes $750,000 of direct premium, cedes 10% under quota share with a 30% commission, and pays $55,000 for an excess-of-loss cover with no commission. Find the total reinsurance premium cost, commission, and net premium after commission. (Answer: total reinsurance premium $130,000; commission $22,500; net $642,500.)
A portfolio has $300,000 in Segment A and $200,000 in Segment B. In Segment A, 40% is ceded facultatively first; then 25% of the remaining Segment A premium is ceded under quota share. In Segment B, 25% is ceded under quota share. The facultative commission is 10% of its ceded premium, and quota-share commissions are 20% of quota-share ceded premium. Find total ceded premium, total commission, and net premium after commission. (Answer: ceded premium $215,000; commission $31,000; net $316,000.)
Gross direct premium is $1,200,000, ceded premium is $240,000, and ceding commission is $36,000. Give both net written premium before commission and net premium after commission. (Answer: before commission $960,000; after commission $996,000.)

What You'll Learn