1.4 Reserving — Provisioning for Claims Not Yet Paid
When an insurer sells a policy, it doesn’t yet know what it will owe, so it sets money aside, called reserves. Case reserves cover claims already reported. IBNR, short for incurred but not reported, covers losses that have happened but have not been reported or fully valued. Actuaries estimate these by tracing how claims developed in past years using loss triangles, with methods like the chain ladder, cross-checked by Bornhuetter-Ferguson. Every dollar change in reserves changes pretax profit by a dollar.
Why it matters: A small change in a guess about the future can swing a whole year’s profit.
Summary: Claims reserves are an insurer’s largest liability: case reserves for reported claims plus IBNR for losses incurred but not yet reported or not yet fully valued. Actuaries estimate them by projecting loss development triangles to ultimate with the chain ladder, cross-checked by Bornhuetter-Ferguson. Every dollar of reserve change moves pretax profit by a dollar.
- In the worked triangle, chain-ladder IBNR is 44.47 on reported losses of 252.8, and 72% of it sits in the newest accident year.
- Bornhuetter-Ferguson replaces the volatile latest-year projection with an expected loss ratio, cutting 2025’s ultimate from 84.01 to 73.05.
- Broad IBNR includes development on known claims (IBNER), reopened claims and claims in transit.
- The chain ladder misleads when case reserving, settlement speed, inflation or large losses change.
- Ignoring a 5% tail understates reserves by 14.86, a third of booked IBNR.
An insurer’s single largest liability on its balance sheet is its claims reserve — money set aside for claims that have already happened (or are expected to happen on already-sold policies) but haven’t yet been fully paid out. Reserving splits into two distinct categories: case reserves (a specific estimate for a known, already-reported claim still being processed) and IBNR — Incurred But Not Reported — reserves for claims that have already happened but haven’t yet even been reported to the insurer, estimated using historical patterns of reporting delay.
The workhorse reserving method, the chain ladder (actuaries call it the development technique), assumes that claims recorded to date will keep developing the way past years did. The data come as a loss development triangle: each row is an accident year (the year the loss events happened) and each column shows reported losses (paid plus case reserves, $ millions) at successive 12-month valuations. Newer years have fewer columns because less time has passed.
| Accident year | 12 months | 24 months | 36 months | 48 months | Factor to ultimate | Ultimate | IBNR |
|---|---|---|---|---|---|---|---|
| 2022 | 40.0 | 56.0 | 63.0 | 64.9 | 1.0000 | 64.90 | 0.00 |
| 2023 | 44.0 | 62.0 | 69.4 | — | 1.0302 | 71.49 | 2.09 |
| 2024 | 48.0 | 66.5 | — | — | 1.1559 | 76.87 | 10.37 |
| 2025 | 52.0 | — | — | — | 1.6156 | 84.01 | 32.01 |
| Total | Reported to date: 252.8 | 297.27 | 44.47 | ||||
Step 1, age-to-age factors (volume-weighted): 12→24 = (56.0 + 62.0 + 66.5) ÷ (40.0 + 44.0 + 48.0) = 184.5 ÷ 132.0 = 1.3977; 24→36 = (63.0 + 69.4) ÷ (56.0 + 62.0) = 132.4 ÷ 118.0 = 1.1220; 36→48 = 64.9 ÷ 63.0 = 1.0302. Step 2, the tail: assume no development after 48 months, a tail factor of 1.000 (an assumption this example returns to below). Step 3, cumulative factors: from 12 months, 1.3977 × 1.1220 × 1.0302 = 1.6156; from 24 months, 1.1220 × 1.0302 = 1.1559. Step 4, ultimates: reported × factor, so 2025’s ultimate = 52.0 × 1.6156 = 84.01. Step 5, IBNR = ultimate − reported: 84.01 − 52.0 = 32.01 for 2025, and 44.47 across all years.
Notice where the reserve sits: 72% of the IBNR (32.01 ÷ 44.47) belongs to the newest year, the one with the least data and the largest multiplier. A 5% error in that single 12→24 factor moves the 2025 ultimate by 52.0 × 1.6156 × 5% ≈ 4.2. That is why actuaries often switch the latest years to the Bornhuetter-Ferguson method, which adds to reported losses only the unreported share of an a priori expected loss: with earned premium of 85.0 and an expected loss ratio of 65%, expected losses are 55.25, the unreported share is 1 − 1 ÷ 1.6156 = 38.1%, so BF IBNR = 55.25 × 38.1% = 21.05 and the 2025 ultimate is 52.0 + 21.05 = 73.05 instead of 84.01. When the two methods disagree this much, the gap itself is information: either 2025 is running hot, or its early reports came in faster than usual.
What “IBNR” contains. In practice the IBNR on a balance sheet is a “broad” figure: it covers losses not yet reported at all (pure IBNR), further development on claims already reported (often called IBNER, because case reserves tend to be set low and grow), reopened claims, and claims reported but not yet recorded. Total unpaid claims = case reserves + broad IBNR. If 20.0 of 2025’s reported 52.0 has been paid (an assumed split; the triangle shows reported losses only), the insurer holds 52.0 − 20.0 = 32.0 of case reserves plus 32.01 of IBNR, 64.01 in all, for a single accident year. Every dollar of that estimate passes straight through the income statement: raising IBNR by $1 cuts pretax profit by $1.
The method is only as good as its central assumption, that the future will develop like the past. These are the situations where that assumption breaks.
| Situation | What changes | Why |
|---|---|---|
| Claims department strengthens case reserves | Early reported losses jump; the chain ladder overstates ultimates | Higher early reports are multiplied by old factors built on weaker case reserves |
| Claims are settled faster than before | Paid-loss triangles overstate ultimates | Payments arrive earlier, but the factors assume the old, slower pattern still applies |
| Inflation or “social inflation” accelerates | Factors understate ultimates | Past factors embed past cost growth; larger jury awards and medical costs hit all open years at once (a calendar-year effect) |
| One very large loss in a year | Factors swing; ultimates for other years distort | Volume-weighted factors are dragged by a single outlier; actuaries cap or exclude large losses and project them separately |
| New line with no history | No usable triangle | Use an expected loss ratio or Bornhuetter-Ferguson with industry patterns until the book’s own data mature |
| Latest year, tiny reported base | Very large cumulative factor amplifies noise | A 1.6× multiplier on thin data magnifies errors; Bornhuetter-Ferguson leans on the expected loss ratio instead |
| Long tail cut off too early | Ultimates understated for every year | Development beyond the triangle’s last column is treated as zero unless a tail factor is added from industry data or curve fitting |
IBNR reserving is one of the most consequential and difficult judgment calls in all of insurance accounting — under-reserving inflates current-period profit but creates a real, deferred liability that eventually surfaces; a sudden, large increase in IBNR reserves is one of the clearest signals that a company’s claims experience is deteriorating faster than its pricing has adjusted for.
If an accident year’s cumulative factor to ultimate is below roughly 1.2 and claims handling has not changed, then rely on the chain ladder. If it exceeds roughly 1.5, then weight Bornhuetter-Ferguson, because the chain ladder multiplies noise. Always run at least two methods, on paid and reported data; when they differ by more than about 10%, find the cause before booking. These thresholds are practitioner heuristics, not rules from a standard. When reading accounts, treat several consecutive years of adverse development as evidence that current reserves are light too.
Assuming the tail is finished. The triangle uses a tail factor of 1.000. If the true tail is 1.05, every ultimate is 5% short: 297.27 × 5% = 14.86 of missing reserve, so booked IBNR of 44.47 should have been a third higher (14.86 ÷ 44.47 = 33%). Those 14.86 were reported as profit and return later as an adverse development charge. Tails can be very long: Berkshire Hathaway’s 2024 shareholder letter says it is still making substantial payments on asbestos exposures that occurred 50 or more years ago. Fit or benchmark a tail factor for every long-tailed line, and disclose it.
What does IBNR mean in insurance?
Incurred but not reported: a reserve for losses that have already happened but that the insurer has not yet heard about, or not yet recorded at full cost. A car accident on December 30 reported in February is the classic case. Balance-sheet IBNR usually also includes expected growth on claims already reported.
How is IBNR calculated?
Usually by projecting each accident year’s reported losses to an ultimate value with development factors from a loss triangle, then subtracting what has been reported. Above, 2025’s reported 52.0 × 1.6156 gives an ultimate of 84.01 and IBNR of 32.01. Actuaries cross-check with Bornhuetter-Ferguson and expected loss ratio methods.
What is adverse reserve development?
An increase in the estimated losses of past accident years, charged against current-year profit; favorable development is a release that adds to it. Repeated adverse development suggests past reserves were too low, while a long run of releases can mean conservative reserving, or reserves used to smooth earnings.
Claims reserves combine case reserves for reported claims with broad IBNR for losses not yet reported or not yet fully valued. The chain ladder projects each accident year’s reported losses to ultimate with development factors, Bornhuetter-Ferguson tempers the volatile latest years with an expected loss ratio, and an omitted tail factor or a change in claims practice can leave reserves short by a large share of IBNR.
Four questions on this chapter. Decide on your answer first, then click “Reveal Answer.”
1. An accident year has $30 million of reported losses at 12 months. Age-to-age factors are 1.5 (12→24) and 1.1 (24→ultimate). What is the chain-ladder IBNR?
- $19.5 million
- $15.0 million
- $49.5 million
- $3.0 million
Reveal Answer
Answer: A. Cumulative factor = 1.5 × 1.1 = 1.65; ultimate = $30m × 1.65 = $49.5m; IBNR = $49.5m − $30m = $19.5m.
2. Expected losses for a new accident year are $40 million and its cumulative development factor is 1.25. What is the Bornhuetter-Ferguson IBNR?
- $10 million
- $8 million
- $32 million
- $50 million
Reveal Answer
Answer: B. Unreported share = 1 − 1 ÷ 1.25 = 20%; BF IBNR = $40m × 20% = $8m.
3. The claims department starts setting case reserves higher on new claims. What does an unadjusted chain ladder on reported losses tend to do?
- Leave the ultimate losses unchanged
- Shift reserves from old years to new ones
- Overstate ultimate losses for recent years
- Understate ultimate losses for recent years
Reveal Answer
Answer: C. Higher early reported losses are multiplied by factors built on weaker past case reserves, inflating projected ultimates.
4. What does broad IBNR include beyond losses not yet reported at all?
- Premium not yet earned on current policies
- Investment income expected on the reserves
- Case reserves on claims already reported
- Expected growth on claims already reported
Reveal Answer
Answer: D. Broad IBNR adds development on known claims (IBNER), reopened claims and claims in transit to pure IBNR.
1.5 Underwriting — Selecting and Pricing Individual Risk
Pricing sets a price for a group; underwriting applies it to one applicant at a time, deciding whether to accept, charge more or decline. It exists to stop adverse selection: if higher-risk people buy the most and the price is based on the average, the pool gets worse, prices must rise, and healthier customers leave, in what is called a death spiral. Moral hazard is different: it is the change in behavior after people are insured. That is handled with deductibles, coinsurance and claim controls.
Why it matters: Insurers must separate who gets in from how people behave once covered.
Summary: Underwriting applies pricing to individual applicants, accepting, rating or declining each risk on its own characteristics. It exists to stop adverse selection, where higher-risk buyers dominate a pool priced on the average and push it into a death spiral. Moral hazard, the change in behavior after the sale, is handled separately with deductibles, coinsurance and claim controls.
- In the worked pool, a single $3,600 price drives out low-risk buyers and leaves a $128,000 loss on the 20 high-risk ones.
- Risk classes priced at each group’s own expected cost keep low-risk buyers in the pool.
- A $1,000 deductible and 20% coinsurance split a $5,000 claim $1,800 to the insured and $3,200 to the insurer.
- The evidence on adverse selection is market-specific: absent in French auto insurance (2000), present in UK annuities (2004).
- Group coverage that is automatic for everyone weakens selection and justifies lighter underwriting.
While actuaries set pricing at the aggregate, pool level, underwriters apply that pricing framework to individual applicants — deciding whether to accept a specific risk at all, and at what specific premium, based on that individual’s own risk characteristics (a smoker versus non-smoker for life insurance; a driver’s accident history for auto insurance). This individual-level risk selection is what prevents adverse selection — the risk that only the worst risks within a population choose to buy insurance, driving the pool’s average claims experience far worse than the actuary’s original pricing assumed.
Adverse selection arises because buyers know things about their own risk that the insurer does not. Take 100 applicants: 80 low-risk people with expected claims of $2,000 a year and 20 high-risk people with expected claims of $10,000. One price for everyone must cover the average: (80 × $2,000 + 20 × $10,000) ÷ 100 = $3,600. Suppose low-risk people will pay at most $3,000, half again their expected cost (an illustrative assumption). They decline, the pool shrinks to the 20 high-risk buyers, and the break-even price jumps to $10,000. If the insurer had kept charging $3,600, each remaining policy would lose $10,000 − $3,600 = $6,400, or $128,000 across the 20. That unraveling is the “death spiral.” Underwriting stops it by sorting applicants into classes priced at their own expected cost, here about $2,000 and $10,000 before loadings, so neither group subsidizes the other.
Moral hazard is the related problem after the sale: insured people take less care, or use more services, because someone else pays. Insurers answer with cost sharing. With a $1,000 deductible (the amount the insured pays first) and 20% coinsurance (the insured’s share of the rest), a $5,000 claim costs the insurer ($5,000 − $1,000) × 80% = $3,200 and the insured $1,000 + $4,000 × 20% = $1,800. The insured’s stake keeps care in the decision, and the deductible removes the many small claims whose handling cost would be out of proportion to their size.
Theory predicts that people with more coverage should have more claims. The evidence is mixed, and the split is itself the lesson. Pierre-André Chiappori and Bernard Salanié tested French auto insurance contracts against accident data and found no evidence of asymmetric information in that market (Journal of Political Economy, 2000): once the insurer’s own rating variables were controlled for, drivers who chose more coverage did not have more accidents. Amy Finkelstein and James Poterba, studying UK annuities, found systematic links between annuity features and later mortality (Journal of Political Economy, 2004), so buyers did select on private knowledge of their longevity, though not through the size of the annuity. Finkelstein and Kathleen McGarry then showed in long-term care insurance that private information can exist even without the predicted correlation: more cautious people were both more likely to buy coverage and less likely to enter a nursing home (American Economic Review, 2006), an “advantageous selection” that offsets the adverse kind. Where selection does bite, it can be large: when Harvard University switched to equal employer contributions across health plans, David Cutler and Sarah Reber estimated a long-run demand response three times the short-run one and a welfare loss of about 2% of baseline health spending (Quarterly Journal of Economics, 1998). The thread running through these four studies is that selection is market-specific: it depends on what buyers know that the rating variables miss, so it has to be measured, not assumed.
If buyers choose whether and how much to buy, and can see something about their risk that your rating variables miss, then assume takers are worse than the population average: rate on observable drivers, require medical evidence or waiting periods for large amounts, and track take-up by segment. If coverage is automatic for a whole group (employer group life, compulsory auto liability), then selection is weak and lighter underwriting is defensible. If claims rise after the sale for reasons the insured controls, then the problem is moral hazard, answered by deductibles, coinsurance and claim controls.
Pricing on the population average when buyers select themselves. The $3,600 price above was right for a pool that never forms. If only the 20 high-risk applicants buy, claims of 20 × $10,000 = $200,000 meet premium of 20 × $3,600 = $72,000: a $128,000 loss, 178% of premium. Price from the expected mix of actual buyers, check early claims by segment, and underwrite the drivers buyers know best.
What is the difference between adverse selection and moral hazard?
Adverse selection happens before the sale: higher-risk people are more likely to buy, so the pool is worse than average. Moral hazard happens after it: once insured, people take less care or use more services. Underwriting and risk classification address the first; deductibles, coinsurance and claims controls address the second.
Why do insurers ask so many questions before issuing a policy?
Each answer captures a driver of expected claims, such as smoking for life coverage or past accidents for auto. Pricing each class at its own expected cost keeps low-risk buyers in the pool, which prevents the premium spiral shown above. Which questions are allowed varies by line and by state.
Why do insurance policies have deductibles?
A deductible leaves the insured paying the first part of each loss, preserving an incentive to avoid losses and removing small claims that cost more to process than they are worth. With a $1,000 deductible and 20% coinsurance, a $5,000 claim costs the insured $1,800 and the insurer $3,200.
Underwriting prices or declines individual applicants so that low-risk buyers are not driven out by a price set for the average, the adverse-selection spiral that can turn a $3,600 price into a $128,000 loss on 20 high-risk policies. Moral hazard after the sale is a separate problem met with deductibles and coinsurance, and research shows the strength of adverse selection varies by market.
Four questions on this chapter. Decide on your answer first, then click “Reveal Answer.”
1. A pool has 60 applicants expected to claim $1,000 a year and 40 expected to claim $4,000. What single price breaks even if everyone buys?
- $2,500
- $1,600
- $3,000
- $2,200
Reveal Answer
Answer: D. (60 × $1,000 + 40 × $4,000) ÷ 100 = $220,000 ÷ 100 = $2,200.
2. A policy has a $500 deductible and 30% coinsurance. How much of a $3,000 claim does the insurer pay?
- $2,500
- $2,100
- $1,750
- $1,250
Reveal Answer
Answer: C. Insurer pays ($3,000 − $500) × 70% = $1,750; the insured pays $500 + $2,500 × 30% = $1,250.
3. Claims on a dental plan rise sharply after members enroll, because they book treatments they had postponed. Which problem is this mainly?
- Moral hazard after the sale
- A tail factor in the reserving
- A death spiral in the pricing
- Basis risk in the coverage
Reveal Answer
Answer: A. Using more services because someone else pays is moral hazard, answered with deductibles, coinsurance and claims controls.
4. What did Chiappori and Salanié (2000) find in French auto insurance?
- A death spiral that forced several insurers out of the market
- No evidence of asymmetric information, given rating variables
- Strong adverse selection among drivers choosing fuller coverage
- Advantageous selection among the most cautious young drivers
Reveal Answer
Answer: B. Their tests found drivers choosing more coverage did not have more accidents after conditioning on the insurer’s rating variables.
- Drehmann, McGuire, Shirakami, Conway and Lovell, Uncovering FX settlement risk, BIS Quarterly Review (June 2026) — PvP 36% ($5.2 trillion a day) and gross bilateral 10% ($1.4 trillion) of FX settlement in April 2025