What is IBNR? Incurred but not reported reserves explained with a worked example

IBNR means “incurred but not reported” and can refer to the claims themselves or the reserve for them. For direct insurers, it may also include expected development on reported claims. Here, “implied IBNR” means a reserve residual inferred from a triangle projection. In the paid-triangle example, it is projected outstanding less separately held case reserves. The article distinguishes this from true IBNR and IBNER (“incurred but not enough reserved”), following the Institute and Faculty of Actuaries’ (IFoA) Claims Reserving Manual. It then works through a chain-ladder calculation and explains where claims provisions appear under Solvency II, including templates S.17.01 and S.19.01. The example is the same kind of calculation that TP Tool runs on your own claim transactions, only much smaller. Actuaries will know the arithmetic.

IBNR and its place in the claims reserve

At any valuation date, a non-life insurer owes money on claims in three states. Some claims have been reported and remain unsettled. Claim handlers hold case reserves on them, which together form the reported but not settled (RBNS) reserve. Some claims have happened but have not yet been reported. And some reported claims will cost more or less than their current case reserves as new information emerges or claims reopen.

The Institute and Faculty of Actuaries’ Claims Reserving Manual distinguishes claims not yet known to the insurer (“true IBNR”) from subsequent development on open claims. It cautions that the terms are not exclusive to reinsurance or direct insurance: direct insurers may also use IBNR to include case-reserve development. In the manual’s convention, let $\mathrm{True\ IBNR}$ denote true IBNR and $\mathrm{Development\ on\ Open\ Claims}$ denote development on open claims. Their sum is IBNER (“incurred but not enough reserved”):

The manual also notes that IBNYR (“incurred but not yet reserved”) has the same meaning as true IBNR. Terminology varies: here, “true IBNR” means incurred claims not yet reported or known. “Implied IBNR” means a reserve residual inferred from a triangle projection. In this paid-triangle example, it is projected outstanding less separately held case reserves. An incurred-triangle projection can also produce a residual, but its incurred starting point already includes case estimates, so the residual has a different interpretation. The implied amount may contain both true IBNR and development on open claims, which aggregate triangle data cannot separate. This article uses IBNER only to describe the IFoA Manual’s convention above, not as a universal synonym for implied IBNR. For accident year $i$, projected outstanding is the projected ultimate less paid claims to date. Let $\mathrm{Outstanding}_i$ denote that amount, $\mathrm{Case\ Reserves}_i$ the separately held case reserve and $\mathrm{Implied\ IBNR}_i$ the residual after deducting case reserves, so:

Under Solvency II, the claims provision’s best estimate covers claim events that have already occurred, whether reported or not. It is a probability-weighted, discounted projection of the future cash flows needed to settle those obligations, including relevant expenses. The premium provision covers future claim events within the existing contract boundary, as set out in the Delegated Regulation.

Why IBNR exists

Two things create it. The first is reporting lag. A motor property damage claim is usually reported within days. A liability claim, an occupational disease or a bodily injury claim can surface months or years after the accident, and a valuation at 31 December always misses the December accidents nobody has reported by the time the books close. The second is late development. Case reserves are set with the information available on the day. Litigation runs its course, and a claim closed for 5,000 is reopened at 50,000.

For short-tail lines such as property, implied IBNR is often small relative to case reserves. For long-tail liability lines it can be larger. These are tendencies, not definitions, and depend on the portfolio and reserving basis.

A worked example: chain-ladder on a paid triangle

The chain-ladder method takes the historical pattern of payments and assumes the open years will follow it. Whether chain-ladder is suitable for a particular portfolio depends on the data and assumptions. This example illustrates the calculation only and does not assess the method’s suitability or predictive performance. Here is a cumulative paid loss triangle for one homogeneous risk group, four accident years and four development years, in EUR thousand. Row 2022 is fully developed, row 2025 has only its first year.

Table 1. Cumulative paid claims by accident year and development year (EUR thousand).

The development factors are volume weighted. For each step, the sum of the later column divided by the sum of the earlier column, using only accident years with both values. Writing $C_{i,j}$ for cumulative paid claims in accident year $i$ and development year $j$, the factor from development year $j$ to $j+1$ is:

where $\mathcal{I}_j$ contains the accident years with observed claims in both development periods. For this triangle:

We assume no payments after development year 4, so the tail factor is $f_{4\to\infty}=1.000$. On a real liability portfolio a tail would arguably be applied. Here it keeps the example short.

Each open accident year is carried from its latest diagonal to ultimate by multiplying through the remaining factors:

For each accident year, the paid triangle supplies a projected ultimate $\mathrm{Ultimate}_i$. Total outstanding on a paid basis is

Subtracting the separately supplied case reserves $\mathrm{Case\ Reserves}_i$ leaves the implied reserve above current incurred. Then one obtains an implied IBNR of

This residual is algebraically the incurred-to-ultimate gap for the same ultimate estimate. Note that fitting on an incurred triangle could produce a different ultimate. The residual may include true IBNR and future development on reported claims, which this aggregate calculation cannot separate. In this example, 2022 has no open claims.

Table 2. Chain-ladder ultimate, outstanding provision and implied IBNR (EUR thousand).

According to chain-ladder, this risk group needs an outstanding claims provision of 2,018, of which 1,450 is already sitting in case reserves and 568 is implied IBNR. The youngest year contributes about two thirds of the implied IBNR (374 out of 568). Its cumulative factor to ultimate is 1.98, and paid claims are about 50.5% of its projected ultimate.

That sensitivity is also a weakness of the method. If the first factor were 1.550 instead of 1.500, only the 2025 projection changes: its ultimate would rise from 2,574 to 2,660, increasing total implied IBNR from 568 to 654, or about 15%. The data provide little experience to distinguish between those first-year factors. Actuaries therefore review individual age-to-age ratios and may compare a Bornhuetter-Ferguson estimate for the youngest years. Bornhuetter-Ferguson combines the development pattern with an a priori expected loss ratio, reducing the dependence of immature-year estimates on early observed development.

IBNR under local GAAP and under the Solvency II best estimate

The 568 above is an implied IBNR estimate from a synthetic paid triangle. It is undiscounted and excludes any separately projected claims-handling expenses. It is not a Solvency II best estimate or necessarily the booked reserve under a local accounting basis. Statutory reserving rules, including any prudence margins, vary by jurisdiction.

Solvency II technical provisions comprise a best estimate and a risk margin. Under Article 77(2) of the Directive, the best estimate is the probability-weighted average of future cash flows, discounted for the time value of money. The projection includes the cash in- and out-flows required to settle the obligations. For non-life business, Article 36 of the Delegated Regulation distinguishes provisions for claims events that have already occurred (reported or not) from premium provisions for future claim events. The implications for this triangle estimate are:

The best estimate is a discounted cash-flow valuation. The undiscounted 2,018 in this example would first need a payment pattern. Future amounts are discounted using the relevant currency-specific risk-free term structure, with applicable Solvency II adjustments where used. Discounting is generally more material for long-tail business.

The best estimate is a probability-weighted average, not an amount with an added margin for prudence. The separately calculated risk margin reflects the cost of holding eligible own funds to support the obligations over their lifetime and is not a discretionary buffer for conservative best-estimate assumptions.

The cash-flow projection includes relevant claims-handling expenses and should reflect material future claim events not adequately represented in the historical data (often called ENIDs, or events not in data). Their expected cash-flow impact should be assessed using suitable evidence and actuarial methods and a fixed uplift needs a defensible basis. The EIOPA Guidelines on valuation of technical provisions address the assumptions and methods, while the Bank of England’s SS5/14 gives UK supervisory guidance.

Solvency II requires the best estimate to be calculated gross. Article 77(2) of the Directive says to make no deduction for amounts recoverable from reinsurance contracts or special purpose vehicles. Article 81 requires those recoverables to be calculated separately. In other words, the claims cash flows in the technical provisions represent the insurer’s full claims obligations, before reinsurance recoveries are taken into account.

This gross view also makes reinsurance credit risk visible. Recoveries depend on the reinsurer paying, so Article 81 requires the recoverable to reflect timing differences and be adjusted for expected counterparty default, based on probability of default and loss-given-default. Netting recoveries against claims cash flows would obscure that exposure.

The 2,018 in this example is not itself a Solvency II best estimate. A regulatory valuation requires dated future cash-flow projections for incurred claims, including relevant expenses and material ENIDs, followed by discounting. The case-reserve and implied-IBNR split is useful for analysis, but Solvency II reports the best estimate of the claims provision rather than a separate IBNR line.

Where IBNR lands in the Solvency II templates

Two templates carry the provision. S.17.01 with non-life technical provisions is submitted quarterly and annually. It reports gross best estimates for premium and claims provisions, reinsurance recoverables after counterparty-default adjustment, net best estimates and the risk margin. IBNR has no separate row and is included in the claims provision. Where applicable, reporting is split by line of business.

Quarterly estimates may need a documented manual correction when material information arrives after quarter-end but before the quarterly return is submitted. For example, a large claim reported after quarter-end may provide evidence about a loss event that had already occurred at the valuation date. Under Solvency II, Article 77(2) requires the best estimate to use up-to-date, credible information and realistic assumptions. An adjustment should reflect conditions at quarter-end. A genuinely new post-quarter-end event is not automatically backdated and should be assessed under the applicable subsequent-event and reporting rules.

S.19.01 is the annual claims-development template. It reports triangles for claims paid, best-estimate claims provisions and RBNS, along with related reinsurance and net information. RBNS covers reported, unsettled claims and excludes IBNR, but need not be valued on a Solvency II best-estimate basis. Comparing it with the best estimate therefore gives only an implied IBNR indicator. The difference may also reflect development on reported claims and differences in measurement basis.

The net best estimate of claims provisions also enters the volume measure for reserve risk in the non-life underwriting risk module, part of the SCR standard formula calculation. Reserving assumptions therefore affect both the technical-provision valuation and the SCR. An estimate too high reduces own funds through higher liabilities and may also increase the SCR. The capital effect depends on the net provisions and the applicable formula, so it is not simply a fixed “double cost”.

Where this lands in the software

TP Tool starts one step earlier than the triangle. Claim and premium transactions are loaded directly, checked for completeness and inconsistencies, and grouped in the Risk Group Designer into the homogeneous risk groups the actuary wants to reserve. The Statistical Engine then builds the run-off triangles for each group and runs for example chain-ladder, Bornhuetter-Ferguson, fixed loss ratio estimates side by side, with the age-to-age factors and diagnostics visible, so the sensitivity is clear. Discounting, inflation and claims handling expenses are applied in the same run, and the results populate S.17.01 and S.19.01 together with S.05.01, S.18.01, S.20.01, S.21.01, S.28.01, S.29.02 and S.29.03, with ECB currency conversion as at the reference date.