Closed and Reopened Claims

Why Closed Claims Can Still Have Future Liability

A claim may be marked closed after the insurer has made the payments currently expected and completed its immediate handling. That status is an administrative description at a point in time, not proof that the claim can never produce another payment. A claimant may return for additional treatment, new information may emerge, or a dispute may resume. If the claim is reopened, future payments can follow.

For reserve estimation, the key distinction is between claims already known to be open at the valuation date and claims currently closed that may reopen later. The first group has a known open-claim status and is estimated using information about those claims. The second group requires an estimate of whether reopening will occur and, if it does, what additional payments may result. The latter estimate is a liability for possible future payments, not a case reserve on a currently open claim.

Definition: A reopened claim is a claim that was previously closed in the insurer’s records and is subsequently returned to active handling. A reopening liability is the estimated unpaid amount at the valuation date for future payments attributable to claims that are currently closed but may reopen. It is distinct from the estimated unpaid amount on claims already open at that date.

In this tutorial, amounts are hypothetical and stated as undiscounted future indemnity payments. Assume that the expected payment amounts already reflect applicable coverage limits, deductibles, and the scope of payments being estimated. Claim adjustment expenses are excluded. If a particular claim is already known to have reopened, its remaining expected payments belong with the estimate for known open claims, not in the estimate for claims still closed.

Estimating Liability From Claims Still Closed

A practical estimate separates three questions: how many currently closed claims may reopen, how often a reopened claim leads to a payment, and how large the future payment is when one occurs. The factors can be estimated separately or combined into one conditional average, provided the definitions and data basis are consistent.

Model: For a homogeneous group of $N$ claims that are currently closed, let $p$ be the probability that a claim reopens, $q$ be the probability of a future payment conditional on reopening, and $s$ be the expected amount of that payment conditional on a payment occurring. Under these definitions, the expected future payment liability for the group is $N p q s$. If $m$ is instead defined as the expected future payment conditional on reopening, including zero for reopened claims with no payment, the equivalent formula is $N p m$, where $m=q s$.

The assumptions matter. The probabilities and expected amounts should apply to the group being estimated and to the valuation date in question. In particular, $s$ must represent future unpaid amounts, not the original total cost of the claim. The formula estimates an expected aggregate amount; it does not assert that the actual number or amount of future payments will equal that expectation.

E[\text{future payments}] = N \times P(\text{reopen}) \times P(\text{payment}\mid\text{reopen}) \times E[\text{payment amount}\mid\text{payment}] = Npqs

For heterogeneous claims, do not force all claims into one average if their reopening patterns or expected payments differ materially. Divide them into appropriate groups and add the group estimates. For claims $j$ with different assumptions, the expected amount is the sum of each claim’s expected future payment.

E[\text{future payments}] = \sum_j p_j q_j s_j

Why the Expected-Value Formula Holds

The formula follows by representing each claim’s future payment with indicator variables. For claim $j$, let $I_j$ equal 1 if it reopens and 0 otherwise; let $J_j$ equal 1 if it produces a future payment after reopening and 0 otherwise; and let $Z_j$ be the amount of that payment when one occurs. The future payment is $I_jJ_jZ_j$. By conditioning on reopening and then on payment, its expected value is $p_jq_js_j$.

E[I_jJ_jZ_j] = P(I_j=1)\,P(J_j=1\mid I_j=1)\,E[Z_j\mid J_j=1,I_j=1] = p_jq_js_j

The total future payment is the sum across claims. Linearity of expectation means the expected total is the sum of the individual expectations. This result does not require the claims to reopen independently; dependence may affect the variability of the total, but not this expected-value calculation. The estimate still depends on using appropriate probabilities and payment assumptions.

Worked Examples

Worked Example: Separating Known Reopened Claims From Closed Claims

A hypothetical insurer has 600 claims that are closed and have not reopened as of the valuation date. For each of these claims, the estimated probability of reopening is 3%. Given reopening, the probability of a future indemnity payment is 80%; if a payment occurs, its expected amount is $5,000. Separately, 4 claims have already reopened and are currently open, with an estimated $7,000 of unpaid indemnity per claim. Estimate the combined unpaid indemnity for these two groups.

Method. Estimate the closed-claim reopening liability with $N p q s$, then add the unpaid estimate for the known open claims. The populations are separate.

Step 1: Estimate expected reopenings among the closed claims. There are $600 \times 0.03=18$ expected reopenings.

Step 2: Allow for reopened claims that produce no future payment. The expected number with a payment is $18 \times 0.80=14.4$. A fractional expected count is appropriate for an aggregate expectation.

Step 3: Estimate the closed-claim liability. The expected amount is $14.4 \times \$5{,}000=\$72{,}000$.

Step 4: Estimate the known open-claim liability. The 4 already reopened claims have estimated unpaid indemnity of $4 \times \$7{,}000=\$28{,}000$.

Step 5: Combine the distinct groups. The combined estimate is $\$72{,}000+\$28{,}000=\$100{,}000$.

Check. The closed-claim portion is also $600 \times 0.03 \times 0.80 \times \$5{,}000=\$72{,}000$; adding the separate $28,000 open-claim estimate gives $100,000. The common mistake this method avoids is either omitting the already reopened claims or counting them again among the currently closed claims.

Worked Example: Segmenting Closed Claims by Reopening Experience

A hypothetical insurer is estimating future payments from two groups of claims that remain closed. Group A has 240 claims: 4% are expected to reopen, and conditional on reopening, 75% are expected to produce a future payment averaging $6,000. Group B has 160 claims: 10% are expected to reopen, and conditional on reopening, 50% are expected to produce a future payment averaging $9,000. Estimate the total liability for these currently closed claims.

Method. Apply the expected-payment formula separately to each group because the assumptions differ.

Step 1: Calculate Group A’s expected payment count. Expected reopenings are $240 \times 0.04=9.6$. Expected claims with a payment are $9.6 \times 0.75=7.2$. Group A’s expected payment amount is $7.2 \times \$6{,}000=\$43{,}200$.

Step 2: Calculate Group B’s expected payment count. Expected reopenings are $160 \times 0.10=16$. Expected claims with a payment are $16 \times 0.50=8$. Group B’s expected payment amount is $8 \times \$9{,}000=\$72{,}000$.

Step 3: Add the group estimates. The total is $\$43{,}200+\$72{,}000=\$115{,}200$.

Check. Direct substitution gives $240(0.04)(0.75)(\$6{,}000)+160(0.10)(0.50)(\$9{,}000)=\$43{,}200+\$72{,}000=\$115{,}200$. The method avoids applying one pooled reopening rate or payment amount to claims with materially different assumptions.

Worked Example: Estimating More Than One Future Payment

A hypothetical insurer has 500 claims that are currently closed and have not reopened. Each has a 6% probability of reopening. Conditional on reopening, the claim is expected to produce an initial future indemnity payment of $3,200. Also conditional on reopening, there is a 25% probability of one additional future payment of $4,000. Estimate the liability for these claims. Assume the additional payment is separate from the initial payment.

Method. First find the expected total payment conditional on reopening; then multiply by the expected number of reopenings. The initial payment is expected for every reopened claim under the stated assumptions.

Step 1: Find the expected additional payment per reopened claim. This is $0.25 \times \$4{,}000=\$1{,}000$.

Step 2: Find the expected total future payment conditional on reopening. This is $\$3{,}200+\$1{,}000=\$4{,}200$.

Step 3: Find the expected number of reopenings. This is $500 \times 0.06=30$.

Step 4: Estimate the liability. The expected amount is $30 \times \$4{,}200=\$126{,}000$.

Check. The initial-payment component is $30 \times \$3{,}200=\$96{,}000$; the additional-payment component is $30 \times 0.25 \times \$4{,}000=\$30{,}000$. Their sum is $126,000. The method avoids treating the additional payment as certain for every reopened claim.

Reopening Estimates and Open-Claim Reserves

A claim’s reserve category depends on its status at the valuation date. If it is already reopened and active, estimate its remaining payments as part of the known open-claim inventory. If it remains closed, its potential future payments belong in the estimate for claims that may reopen. These are different populations and should be identified before calculations are combined.

For a combined estimate, a useful structure is:

\text{Unpaid indemnity estimate} = \text{estimate for currently open claims} + \text{estimated future payments from claims still closed}

This structure is valid only when the two components are mutually exclusive and each measures future unpaid amounts at the same valuation date and on the same basis. Past payments are not part of an unpaid liability. Nor should the original total cost of a claim be used as the expected future payment if some of that cost has already been paid.

Key takeaway: A closed claim can contribute to an unpaid liability through the possibility of reopening. Estimate that liability from future unpaid payments, using reopening and payment assumptions appropriate to the closed claims. Keep it separate from estimates for claims already open, and combine the components only after checking that there is no overlap.

Common Mistakes and Exam Traps

Treating closure as proof of zero future liability. Closure is a recorded status; it does not rule out later reopening.
Using original claim severity instead of future payment severity. An unpaid estimate concerns payments after the valuation date, not amounts already paid.
Applying the payment probability to the wrong group. If $q$ is conditional on reopening, use $p q$, not $p+q$ or $q$ alone.
Double counting known reopened claims. Remove claims already open from the group used to estimate future reopenings, or otherwise reconcile the populations explicitly.
Assuming a reopening always generates a payment. If some reopenings produce no payment, reflect that possibility in $q$ or in the conditional expected amount.
Ignoring differences among claim groups. When reopening rates or future payment amounts differ, estimate by segment and add the results rather than applying an unsupported overall average.

Check Your Understanding

For each problem, estimate future unpaid indemnity as of the stated valuation date. Treat all amounts as undiscounted and use only the populations described.

A hypothetical insurer has 300 currently closed claims. Each has a 4% chance of reopening; given reopening, the chance of a future payment is 50%, with an average payment of $10,000. What is the expected liability? (Answer: $60,000)
There are 8 known reopened claims with estimated unpaid indemnity of $3,500 each. Separately, 400 claims remain closed; 2.5% are expected to reopen, and 80% of reopened claims are expected to produce a payment averaging $6,000. What is the combined estimate? (Answer: $76,000)
A closed-claim portfolio has two segments. Segment A has 100 claims, a 10% reopening probability, a 60% payment probability after reopening, and a $5,000 average payment. Segment B has 200 claims, a 2% reopening probability, a 50% payment probability after reopening, and an $8,000 average payment. What is the total expected liability? (Answer: $46,000)
A hypothetical insurer has 12 known reopened claims, each with an estimated $7,500 unpaid. It also has 250 claims that remain closed, with a 4% reopening probability, a 75% payment probability after reopening, and a $4,000 average payment. What is the combined estimate? (Answer: $120,000)
Among 1,000 claims that remain closed, 3% are expected to reopen. For each reopened claim, an initial future payment of $2,000 is expected, and there is a 50% probability of an additional separate $3,000 payment. What is the expected liability? (Answer: $105,000)

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