Introduction
An insurer may transfer some of the financial consequences of its policies to another insurer. The transfer creates a second relationship: the original insurer has obligations to its policyholders, while the reinsurance agreement specifies amounts due between the insurers. Keeping these relationships separate is essential. A ceded premium is not a claim recovery, and a reinsurance recovery does not, by itself, change the amount the original insurer owes its policyholder.
This tutorial establishes the parties and cash-flow terminology used to describe reinsurance. The examples are deterministic accounting illustrations: they use only the contract amounts stated, with no assumed interest, expenses, taxes, or timing adjustments. No probability distribution is required.
Two Relationships, Two Sets of Cash Flows
In a typical indemnity reinsurance arrangement, the policyholder pays the policy premium to the ceding insurer. If a covered claim occurs, the ceding insurer remains responsible for settling the policyholder’s claim under the original policy. The reinsurance agreement is a separate contract: it determines whether and how much the reinsurer owes the ceding insurer. Depending on the agreement and claim-handling arrangements, a reinsurer may pay the ceding insurer after the ceding insurer pays the claim, or payment timing may be organized differently. The essential accounting distinction remains the same.
The premium flow runs from the ceding insurer to the reinsurer: the ceding insurer pays the agreed ceded premium. The claim flow runs in the opposite direction when the agreement provides a recovery: the reinsurer pays the agreed ceded loss or claim recovery to the ceding insurer. “Ceded loss” names the portion assigned to the reinsurer; it does not mean the policyholder’s claim has been reduced.
| Amount | Meaning | Typical direction |
|---|---|---|
| Gross premium | Premium collected on the original policy before reinsurance | Policyholder to ceding insurer |
| Ceded premium | Premium owed under the reinsurance agreement | Ceding insurer to reinsurer |
| Retained premium | Gross premium less ceded premium | Remains with ceding insurer before other expenses |
| Gross loss | Claim amount under the original policy before reinsurance | Ceding insurer to policyholder or claimant |
| Ceded loss | Claim amount recoverable from the reinsurer under the agreement | Reinsurer to ceding insurer |
| Retained loss | Gross loss less the reinsurance recovery | Ultimately borne by ceding insurer |
For a claim that is fully within the scope of the reinsurance agreement, with a recovery no greater than the gross claim, the basic accounting identities are:
These equations describe amounts, not necessarily the precise dates on which money moves. They also do not account for commissions, expenses, taxes, or other adjustments unless those items are explicitly included in the stated amounts.
Worked Example: Separating Premium Cession from Claim Recovery
A hypothetical insurer collects a gross premium of $1,500 on a policy. Its reinsurance agreement assigns $450 of that premium to the reinsurer. A covered claim has a gross amount of $1,000, and the agreement specifies a $300 recovery from the reinsurer. Find the retained premium and retained loss.
Method. Apply the premium identity to the two premium amounts and the loss identity to the two claim amounts. Do not use the ceded premium to calculate the claim recovery.
Retained premium. The gross premium is $1,500 and the ceded premium is $450, so \(1{,}500-450=1{,}050\). The ceding insurer retains $1,050 before other expenses.
Retained loss. The gross loss is $1,000 and the ceded loss is $300, so \(1{,}000-300=700\). The ceding insurer retains $700 of this claim.
Check. The premium amounts reconcile because \(1{,}050+450=1{,}500\). The claim amounts reconcile because \(700+300=1{,}000\). The reinsurer receives $450 of premium and owes $300 for the claim under the stated terms; these are separate cash flows.
Why the Retained-Amount Identities Hold
The identities follow from partitioning each gross amount between the ceding insurer and the reinsurer. For a premium, the gross amount is allocated into the part retained and the part ceded. Rearranging that allocation gives the retained-premium formula. For a covered loss, the gross claim is allocated into the part ultimately borne by the ceding insurer and the part reimbursed by the reinsurer. Rearranging gives the retained-loss formula.
This is an accounting reconciliation, not a rule that determines the contract’s ceded amounts. The reinsurance agreement determines those amounts; once they are known, subtraction gives the retained amounts. If a claim is outside the agreement, or an amount is not recoverable under its terms, it must not be included as a ceded loss. In an ordinary indemnity setting, a recovery for a particular claim cannot exceed the covered gross loss being allocated.
Record the gross premium and the gross claim amount before reinsurance.
Identify the ceded premium and any ceded loss or recovery specified by the agreement.
Subtract the ceded premium from gross premium and the ceded loss from gross loss.
Check that retained plus ceded equals gross for premiums and for losses.
Working with Claim Schedules and Portfolio Totals
A reinsurance agreement may specify different ceded amounts for different policies or claims. The ceding insurer should therefore calculate or read the ceded amount for each item according to the agreement before adding the results. The same accounting identities apply to totals: sum the gross amounts, sum the ceded amounts, and subtract to obtain the retained totals. A valid aggregate reconciliation should also match the sum of the claim-by-claim retained amounts.
The ceded premium and ceded loss are not interchangeable. The former is the price paid for reinsurance; the latter is an amount recoverable when a covered loss occurs. Their difference can be useful when reconciling a period’s cash flows, but it is not automatically a profit measure: expenses, claim timing, reserves, and other accounting items may matter.
Worked Example: Reconciling Two Claims to a Total
A hypothetical ceding insurer has two claims. The reinsurance schedule specifies a recovery of $250 on the first gross claim of $900 and $1,100 on the second gross claim of $2,000. Calculate the retained loss for each claim and in total. Assume the scheduled recoveries are valid under the agreement and there are no other adjustments.
First claim. Retained loss is \(900-250=650\). Check: \(650+250=900\).
Second claim. Retained loss is \(2{,}000-1{,}100=900\). Check: \(900+1{,}100=2{,}000\).
Aggregate calculation. Total gross loss is \(900+2{,}000=2{,}900\). Total ceded loss is \(250+1{,}100=1{,}350\). Thus total retained loss is \(2{,}900-1{,}350=1{,}550\).
Check. Adding the claim-level retained amounts gives \(650+900=1{,}550\), matching the aggregate result. Also, \(1{,}550+1{,}350=2{,}900\). The method avoids subtracting one claim’s recovery from another claim or treating a recovery as a reduction in the policyholder’s gross claim.
Worked Example: Reinsurance Cash-Flow Reconciliation for a Period
Over a hypothetical accounting period, an insurer collects $24,000 of gross premiums and pays $5,500 of ceded premium. It has $15,000 of gross claims and receives $4,200 of reinsurance recoveries. Find the retained premium, retained loss, and retained underwriting balance before expenses. Assume all amounts relate to the same period and no other items apply.
Retained premium. Subtract ceded premium from gross premium: \(24{,}000-5{,}500=18{,}500\).
Retained loss. Subtract recoveries from gross claims: \(15{,}000-4{,}200=10{,}800\).
Retained balance before expenses. Subtract retained loss from retained premium: \(18{,}500-10{,}800=7{,}700\).
Independent check. Before reinsurance, gross premiums less gross claims equal \(24{,}000-15{,}000=9{,}000\). The reinsurer receives $5,500 of ceded premium and pays $4,200 of recoveries, a net $1,300 cash outflow from the ceding insurer. Subtracting that outflow from the gross balance gives \(9{,}000-1{,}300=7{,}700\), agreeing with the retained calculation. This is a balance before expenses, not necessarily underwriting profit.
Common Mistakes and Exam Checks
- Subtracting ceded premium from a claim. Premium and loss are different quantities. Calculate retained premium from premium amounts and retained loss from claim amounts.
- Assuming a recovery changes the policyholder’s claim. The gross claim remains the amount due under the original policy. The recovery is a separate amount due under the reinsurance agreement.
- Calling every gross claim a ceded loss. Only the amount recoverable under the agreement is ceded; the rest is retained by the ceding insurer.
- Mixing periods or units. Reconcile amounts for the same set of policies, claims, and time period, and convert units before adding.
- Calling a premium-minus-loss balance profit. Unless all relevant expenses and adjustments are included, this is only a balance before those items.
A reliable solution labels each amount before calculating: gross premium, ceded premium, retained premium, gross loss, ceded loss, and retained loss. Then check both equalities independently. This simple discipline prevents the most consequential errors in tracing reinsurance cash flows and is aligned with the SOA Exam FAM (Fundamentals of Actuarial Mathematics) syllabus.
Check Your Understanding
For each item, use only the amounts stated. Unless noted otherwise, assume the ceded amounts are valid under the reinsurance agreement and ignore expenses, taxes, interest, and timing adjustments.
- A ceding insurer has a gross premium of $950 and owes $190 of ceded premium. A claim has a gross loss of $620 and a ceded loss of $155. Find retained premium and retained loss. (Answer: retained premium $760; retained loss $465.)
- During one period, gross premiums are $32,000 and ceded premiums are $7,200. Two gross claims are $11,500 and $19,000, with recoveries of $2,300 and $6,800, respectively. Find total retained premium and total retained loss. (Answer: retained premium $24,800; retained loss $21,400.)
- A hypothetical insurer has gross premium $5,000, ceded premium $1,250, gross loss $4,200, and ceded loss $900. Find the retained balance before expenses. Check it by starting with gross premium less gross loss and adjusting for the reinsurer’s net cash flow. (Answer: $450; gross balance $800 less net reinsurance outflow $350.)
- A calculation incorrectly finds retained loss by subtracting a $600 ceded premium from a $1,900 gross claim. The ceded loss is actually $500; gross premium is $2,400. Find the correct retained loss and retained premium, and state the error. (Answer: retained loss $1,400; retained premium $1,800; the claim calculation must use ceded loss, not ceded premium.)
- For two policies, gross premiums are $8,000 and $12,000; ceded premiums are $1,100 and $2,400. Gross claims are $5,000 and $14,000; recoveries are $900 and $3,500. Find total retained premium, total retained loss, and the retained balance before expenses. (Answer: retained premium $16,500; retained loss $14,600; retained balance $1,900.)