Ceded Case Reserves and Outstanding Recoverables

Introduction

A gross case reserve estimates the unpaid amount on a reported claim. It is not automatically the amount recoverable from a reinsurer: the treaty may cede only a share of covered losses, or may respond only above an attachment point. For an excess-of-loss claim, even a case estimate below attachment can have a positive expected recovery if the ultimate loss is uncertain.

The central task is to compare the ceded amount implied by the current estimate of the claim with any recovery already recognized or paid. That comparison must follow the treaty’s covered-loss definition, attachment, limit, and payment basis. The methods below assume the claim is eligible under the treaty and focus on estimating the outstanding recovery from case reserves, not on estimating unreported claims.

Definition: For a reported claim, let $P$ be gross covered loss paid to date and $C$ be the gross case reserve for additional covered loss. The incurred-to-date estimate is $P+C$. A ceded outstanding recoverable is the estimated total treaty recovery on the claim less the recovery already paid or recognized, subject to the treaty terms. It is not necessarily a fixed percentage of $C$.

Proportional Treaties: Apply the Share to Unpaid Loss

Under a proportional treaty, the reinsurer pays a specified share $q$ of eligible covered loss, where $0\le q\le1$. Assume the share is constant, the claim is covered, and the case reserve measures unpaid loss on the same basis as the treaty. Then the ceded case reserve is $qC$. Past recoveries on paid losses do not reduce this amount: they relate to payments already made, not to the current unpaid reserve.

\text{Ceded outstanding case reserve}=qC

This direct calculation does not include a ceding commission, which is generally a separate premium-side or accounting item. If the treaty has exclusions, a special definition of covered loss, or a different allocation basis, first determine the treaty-eligible part of the case reserve and apply the share to that amount.

Worked Example: Quota Share Recoverable on Several Case Reserves

A hypothetical insurer has three reported claims covered by a 25% quota share. Their gross case reserves are $48,000, $72,000, and $40,000. All amounts are covered loss, and no special exclusions apply. Estimate the ceded outstanding case reserve.

Method. Apply the treaty share to each claim’s unpaid covered loss. Because the share is constant, the claim-level amounts can also be summed and multiplied by the share.

First sum the gross case reserves:

C_{\mathrm{total}}=\$48{,}000+\$72{,}000+\$40{,}000=\$160{,}000.

The ceded amounts by claim are $0.25(\$48{,}000)=\$12{,}000$, $0.25(\$72{,}000)=\$18{,}000$, and $0.25(\$40{,}000)=\$10{,}000$. Therefore:

\text{Ceded outstanding}=\$12{,}000+\$18{,}000+\$10{,}000=\$40{,}000.

Check. $0.25(\$160{,}000)=\$40{,}000$, agreeing with the claim-by-claim result. This method avoids the mistake of subtracting recoveries already received on paid losses from the current case reserve.

Excess of Loss: Recalculate the Layer Recovery

For a per-risk excess-of-loss treaty with attachment $a$ and limit $L$, the recovery on a covered loss amount $x$ is the amount in the layer from $a$ to $a+L$. Assume the treaty applies to the claim’s cumulative covered loss, the limit is available for that claim, and paid loss and case reserve use the treaty’s covered-loss basis. Define:

g(x)=\min\{\max(x-a,0),L\}.

If paid loss $P$ has already generated a recovery of $g(P)$, and the estimated ultimate covered loss is $P+C$, the estimated outstanding recovery is the difference between the recovery at the estimated ultimate and the recovery on paid loss:

\text{Ceded outstanding}=g(P+C)-g(P).

This formula assumes that recoveries are recognized consistently with the treaty’s loss basis and that $g(P)$ represents the amount already paid or recognized. If the actual amount already recognized differs—for example, because of prior adjustments—use the actual recognized amount as the subtraction, while estimating the ultimate recovery under the treaty.

Why the difference is the right amount: Under the stated assumptions, the layer has paid $g(P)$ on the loss already paid. When the claim develops to $P+C$, the total layer obligation is $g(P+C)$. The unpaid portion is the total obligation less the portion already satisfied, so it is $g(P+C)-g(P)$. The difference cannot exceed $C$, since an additional dollar of gross loss can produce at most one additional dollar of layer recovery.

The subtraction matters when the paid loss has already entered the layer. Simply applying the layer formula to the case reserve would treat the reserve as if it were the claim’s total loss, rather than the additional loss expected after the paid amount. Also, once the layer is exhausted, further gross case reserve does not create further recovery under that layer.

Worked Example: Outstanding Recovery When the Layer Is Partly Exhausted

A hypothetical per-risk treaty covers each eligible claim excess of $100,000, subject to a $50,000 limit. A reported claim has $120,000 of covered loss paid and a gross case reserve of $40,000. Assume no aggregate limit or other feature changes the per-risk recovery. Estimate the outstanding ceded recoverable.

Method. Calculate the layer recovery on paid loss and on the estimated ultimate, then subtract the recovery already attributable to paid loss.

The estimated ultimate covered loss is:

P+C=\$120{,}000+\$40{,}000=\$160{,}000.

At the estimated ultimate, the amount above the $100,000 attachment is $60,000, but the recovery is capped at $50,000:

g(\$160{,}000)=\min\{\$60{,}000,\$50{,}000\}=\$50{,}000.

On the $120,000 already paid, the amount above attachment is $20,000, below the layer limit:

g(\$120{,}000)=\min\{\$20{,}000,\$50{,}000\}=\$20{,}000.

Thus the outstanding recoverable is:

\$50{,}000-\$20{,}000=\$30{,}000.

Check. The remaining layer capacity is $\$50{,}000-\$20{,}000=\$30{,}000$, so the calculated recoverable does not exceed either the $40,000 case reserve or the remaining capacity. A common error is to apply the layer to the case reserve alone: $\min\{\max(\$40{,}000-\$100{,}000,0),\$50{,}000\}=0$. That is wrong because the attachment applies to cumulative covered loss, including the $120,000 already paid.

When the Point Estimate Is Below Attachment

Applying the layer formula to a single estimate is appropriate when the task calls for a deterministic estimate based on that point estimate. If the current estimated ultimate $P+C$ is below $a$, that calculation gives zero. But zero under the point estimate does not necessarily mean zero expected recovery. If ultimate loss is uncertain, some plausible outcomes may exceed attachment.

To estimate expected recovery, specify a probability model for the ultimate covered loss $X$, conditional on the information available. Under the same per-risk treaty assumptions, if $P$ is known and paid recoveries follow $g(P)$, then:

\text{Expected outstanding recoverable} = E[g(X)\mid\text{available information}]-g(P).

The distribution must represent ultimate covered loss on the treaty’s basis, not merely the unpaid reserve, unless the model is explicitly built for unpaid loss and is translated to cumulative loss consistently. In particular, applying $g$ to the mean of $X$ is generally not equivalent to taking the expected value of $g(X)$, because the layer function changes slope at attachment and at exhaustion.

Worked Example: Expected Recovery Before the Point Estimate Reaches Attachment

For a hypothetical per-risk treaty, the attachment is $100,000 and the limit is $30,000. A covered claim has $60,000 paid and a $30,000 gross case reserve, so its point estimate of ultimate loss is $90,000, below attachment. For this illustration, model the claim’s ultimate covered loss $X$, conditional on current information, as Uniform($60,000, $120,000). Estimate the expected outstanding recovery. Assume no recovery has been paid on the claim.

Method. Calculate the expected layer payment over the specified loss distribution. The model’s mean is $(\$60{,}000+\$120{,}000)/2=\$90{,}000$, matching the point estimate, but outcomes above $100,000 can produce recoveries.

For $X\le \$100{,}000$, recovery is zero. For losses between $100,000 and $120,000, recovery is $X-\$100{,}000$. The layer limit is $30,000, and the maximum possible recovery in this distribution is only $20,000, so the limit is not exhausted. The uniform density is $1/\$60{,}000$. Therefore:

\begin{aligned} E[g(X)] &=\frac{1}{\$60{,}000}\int_{\$100{,}000}^{\$120{,}000} (x-\$100{,}000)\,dx\\ &=\frac{1}{\$60{,}000}\left[\frac{(x-\$100{,}000)^2}{2}\right]_{\$100{,}000}^{\$120{,}000}\\ &=\frac{\$200{,}000{,}000}{\$60{,}000} =\$3{,}333.33. \end{aligned}

Since $P=\$60{,}000$ is below attachment, $g(P)=0$. Expected outstanding recovery is therefore $3,333.33. The deterministic point-estimate method would give $g(\$90{,}000)=0$, which is a different answer to a different question. The expected-value result depends on the stated uniform model; it is not justified merely because a case reserve exists.

Check. The probability of exceeding attachment is $(\$120{,}000-\$100{,}000)/\$60{,}000=1/3$, and the average recovery conditional on exceeding attachment is $10,000. Their product is $(1/3)(\$10{,}000)=\$3,333.33$, confirming the integral.

Practical Calculation Sequence and Limitations

A disciplined claim-level calculation helps separate the estimate of gross unpaid loss from the treaty calculation. For an excess-of-loss claim, use the cumulative loss position to identify whether attachment has been reached and how much capacity remains. For a proportional claim, apply the contractual share to eligible unpaid loss.

Confirm treaty eligibility.
Identify the covered claim and determine which parts of the gross case reserve meet the treaty’s loss definition.

Separate paid from unpaid loss.
Record gross covered paid loss $P$, gross covered case reserve $C$, and any ceded recovery already paid or recognized.

Apply the treaty basis.
For a proportional share, apply the share to eligible unpaid loss. For excess of loss, calculate the recovery at the estimated ultimate and compare it with recovery on paid loss.

Use uncertainty only when specified.
If estimating expected recovery rather than a point-estimate recovery, state the conditional ultimate-loss model and average the treaty recovery over that model.

Check limits and balances.
Reconcile the result with the remaining case reserve, remaining layer capacity, and amounts already paid or recognized.

These calculations rely on the stated treaty structure. An annual aggregate limit, reinstatement, multiple inuring treaties, or an allocation rule that changes the covered loss can make a simple claim-level layer calculation insufficient; the remaining treaty balance and applicable terms must then be incorporated. A calculated recoverable is also an estimate of the contractual amount, not a conclusion about whether the reinsurer will ultimately pay it.

Key takeaway: A proportional treaty generally cedes a fixed share of eligible unpaid case loss. For an excess-of-loss treaty, estimate the outstanding amount by comparing the layer recovery on projected ultimate loss with the recovery already attributable to paid loss. If the point estimate is below attachment, a positive expected recovery requires an explicit model for ultimate-loss uncertainty.

Check Your Understanding

For each problem, assume the stated amounts are covered loss and there are no treaty features beyond those specified.

A hypothetical 30% quota share applies to gross case reserves of $50,000 and $85,000. What is the total ceded outstanding case reserve? (Answer: $40,500)
A per-risk layer attaches at $250,000 and has a $150,000 limit. A claim has $180,000 paid and a $100,000 case reserve. Estimate the outstanding recovery using a point estimate of ultimate loss. (Answer: $30,000)
A per-risk layer attaches at $200,000 and has a $100,000 limit. A claim has $280,000 paid and a $100,000 case reserve. The recovery on paid loss has already been recognized. What is the ceded outstanding recoverable? (Answer: $20,000)
A per-risk layer attaches at $120,000 and has a $30,000 limit. Paid loss is $80,000, and ultimate covered loss $X$, conditional on current information, is Uniform($80,000, $160,000). No recovery has been paid. Find the expected outstanding recoverable. (Answer: $9,375)
A per-risk layer attaches at $90,000 and has a $40,000 limit. Paid loss is $100,000 and the case reserve is $70,000. The recoverable on paid loss has been recognized. Calculate the ceded outstanding amount and explain the limiting factor. (Answer: $30,000; the estimated ultimate recovery is capped at $40,000, of which $10,000 is already attributable to paid loss.)

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