If you manage risk or finance at a self-insured organization, you receive an actuarial reserve estimate at least once a year. That estimate tells you how much money you need to hold for claims that have already occurred but have not yet been fully paid. The number matters because it hits your balance sheet, drives your funding decisions, and shapes your insurance program renewal.
But the number is not a fact. It is the output of a method, and the method makes assumptions. If you understand what those assumptions are, you can ask the right questions. If you do not, you are trusting a black box.
This article introduces the five core methods actuaries use to estimate unpaid claims, explains the assumption each one makes, and gives you a framework for understanding which method your actuary relied on and why.
The one equation behind every method
Every reserve estimate, regardless of method, is solving for the same quantity: ultimate claims.
Ultimate claims = paid claims + case outstanding + IBNR
Paid claims are dollars already out the door. Case outstanding (also called case reserves) is the adjuster’s current estimate of what remains on each known open claim. IBNR is everything else: the expected development on known claims plus the claims that have happened but not yet been reported.
The five methods below all estimate ultimate claims. They differ only in what signal they trust to get there. Some lean on historical development patterns. Others lean on an external expectation of what losses should look like. Most actuarial reviews run several methods in parallel and then select a final answer, by accident year, from among them.
Friedland puts it directly: “No single method can produce the best estimate in all situations” (Friedland, p. 345). Every method has a sweet spot and a failure mode. The rest of this article maps both.
Method 1: Chain Ladder (Development Technique)
The bet: the past development pattern is the best predictor of future development.
The chain ladder is the most commonly used reserving method. The actuary takes a loss development triangle, calculates age-to-age factors from historical experience, chains them together into a cumulative development factor (often called an LDF or CDF), and multiplies the current diagonal by that factor to project ultimate claims.
When it works. The chain ladder performs well when the underlying process has been stable: claim processing speeds have not changed, case reserve adequacy has not drifted, the mix of claim types is consistent, and policy limits and retentions are the same across the experience period. When all of these hold, the historical pattern is a reliable guide to the future.
When it breaks. Any change to the process that generated the triangle invalidates the pattern. A shift in case reserve adequacy inflates or deflates the reported triangle’s development factors. A change in settlement speed distorts the paid triangle. A new TPA with different reserving practices introduces a structural break. And a single large claim early in an accident year can swing a thin triangle’s projection by millions.
Self-insured wrinkle. Self-insured programs tend to have thinner data than carrier books. That makes the cumulative development factors for recent accident years highly leveraged. A paid triangle for a bodily injury program might show a CDF of 90.00 on the latest accident year, meaning the projection is ninety times the current paid amount. When the multiplier is that large, small movements in the base create enormous swings in the projected ultimate.
Method 2: Expected Claims Technique
The bet: an externally derived claim estimate is more reliable than the data in the triangle.
The expected claims method bypasses the triangle entirely for immature accident years. The actuary selects an expected claim ratio (sometimes called expected loss ratio; Friedland uses “claim ratio” because she reserves “loss” for non-claims economic concepts) based on pricing, industry benchmarks, or a trended version of the insured’s own mature-year experience, then multiplies it by earned premium or some other exposure base to produce the ultimate.
When it works. This method is most useful for the very newest accident years, where the triangle has little or no meaningful data, or for a new program with no loss history at all. It is also useful when the triangle data is unreliable because of known operational changes.
When it breaks. The expected claim ratio is an assumption, not a calculation. If the selected ratio is wrong, the estimate is wrong, and no amount of development data will correct it within this method. The method ignores actual reported experience entirely, which means it cannot self-correct as information arrives.
Self-insured wrinkle. For a self-insured program with a new TPA, new claims management protocol, or a structural change in the workforce, the expected claims method may be the only defensible approach for the first accident year. But the expected ratio must come from somewhere credible. Ask where.
Method 3: Bornhuetter-Ferguson
The bet: a blend of the development pattern and the expected claim ratio, weighted by maturity, produces a more stable estimate than either input alone.
Bornhuetter-Ferguson (BF) is a credibility-weighted combination of the chain ladder and the expected claims technique. For immature accident years, it leans heavily on the expected claim ratio. For mature years, it leans heavily on actual development. The weight assigned to each input is driven by the CDF: the higher the remaining development factor, the more the method relies on the a priori expectation rather than the reported data.
Mechanically: Ultimate = actual reported + (expected claims x percent unreported). The percent unreported is 1 minus the reciprocal of the cumulative development factor, drawn from the same pattern the chain ladder uses. Actuaries rely on BF almost as often as they rely on the chain ladder (Friedland, p. 152).
When it works. BF shines for recent accident years where the chain ladder is too volatile and the expected claims method ignores useful data that has already emerged. It is the natural default for the most recent one or two accident years in most self-insured reserve reviews.
When it breaks. BF inherits the failure modes of both parent methods. If the expected claim ratio is wrong, the estimate for immature years carries that error. If the development pattern is wrong, the credibility weights are off. A particularly dangerous failure occurs when a CDF falls below 1.00 (which can happen with salvage and subrogation recoveries), because the credibility logic inverts: the method would assign more than 100% weight to the development signal, which makes no mathematical sense. Practitioners floor the CDF at 1.00 to prevent this.
Self-insured wrinkle. BF is the workhorse method for self-insured programs precisely because it anchors volatile recent-year estimates to a defensible a priori while still incorporating the information that has emerged so far. If your actuary is not running BF alongside the chain ladder for your most recent accident years, ask why.
Method 4: Cape Cod
The bet: the data itself can produce a better expected claim ratio than an external assumption.
Cape Cod is a close relative of BF. The difference is where the expected claim ratio comes from. In BF, the actuary selects the expected ratio externally (from pricing, benchmarks, or judgment). In Cape Cod, the ratio is estimated from the triangle data itself, using all accident years weighted by their used-up premium (the portion of premium that corresponds to development reported so far).
When it works. Cape Cod is useful when the actuary does not have a strong external basis for the expected ratio but has enough accident years in the triangle to let the data speak. It automatically adjusts the a priori as new diagonals are added, which makes it less sensitive to a one-time poor initial assumption.
When it breaks. If all accident years in the triangle share the same systematic bias (for example, a multi-year trend in claim severity that the model does not adjust for), Cape Cod will embed that bias in the estimated ratio. It also requires enough data to produce a stable weighted ratio, which some small self-insured programs may not have.
Method 5: Frequency-Severity
The bet: decomposing losses into claim counts and average cost per claim produces a more diagnostic and stable estimate.
Instead of projecting aggregate dollar losses, the frequency-severity method projects claim counts (frequency) and average cost per claim (severity) separately, then multiplies them to get ultimate losses. Each component gets its own development triangle and its own set of development factors.
When it works. Frequency-severity is particularly useful for lines where severity is volatile and frequency is stable. Commercial auto bodily injury is a classic example: claim counts close in a relatively predictable pattern, but average severity is subject to large-loss leverage and verdict-size inflation. Projecting the two components separately can produce a more stable estimate than projecting aggregate losses directly.
When it breaks. The method requires claim count data that is reliably coded and consistently defined across the experience period. If the definition of a “claim” changed (for example, if the TPA started counting incidents differently, or if reopened claims are treated inconsistently), the frequency triangle is corrupted. It also adds complexity: two triangles to evaluate, two sets of assumptions, and a multiplication that can amplify errors in either component.
The decision matrix: which method for which situation
No single method dominates in all situations. The choice depends on the maturity of the accident year and the characteristics of the data. The following matrix illustrates how most practicing actuaries map methods to situations. This is a common framework, not a universal rule.
| Situation | Primary method | Backup method |
|---|---|---|
| Oldest accident years, stable data | Chain ladder (reported) | Chain ladder (paid) |
| Middle-maturity years, stable data | Chain ladder (reported or paid) | Bornhuetter-Ferguson |
| Most recent 1 to 2 accident years | Bornhuetter-Ferguson | Cape Cod or expected claims |
| New program, no loss history | Expected claims | None (single method only) |
| Line with volatile severity (e.g., auto BI) | Frequency-severity | Chain ladder as cross-check |
| Known operational change in experience period | Expected claims or BF | Chain ladder on adjusted data |
The actuary’s report should tell you, for each accident year, which method was selected and why. If it does not, you are missing the most important piece of the analysis.
There is no single right way for an actuary to select ultimate claims from among these methods. Two qualified actuaries reviewing the same data can legitimately arrive at different selections, sometimes materially different, because they weigh the same evidence differently. That is not a flaw in the process. It is a feature of an estimation problem where the true answer is not yet known and will not be known for years.
What a buyer should ask their actuary
These five questions should be part of every reserve review conversation. Each one tests whether the actuary has done more than run the software.
1. Which method drove the selected ultimate for each accident year, and why? A good answer names the method, describes what the data looked like, and explains why the selected method was preferred over the alternatives. A bad answer says “professional judgment” and stops there.
2. Where do the chain ladder and BF estimates diverge, and what does the gap tell you? When the two methods agree, the estimate is well-supported. When they diverge, one of the underlying assumptions is under stress, and the actuary should be able to explain which one and how it affected the selection.
3. What expected claim ratio is being used in the BF or expected claims method, and where did it come from? The ratio is an input, not an output. If it was derived from pricing, from benchmark data, or from the insured’s own mature experience, the derivation should be documented. If it was “carried forward from last year,” ask what would change it.
4. How sensitive is the most recent accident year’s estimate to the selected development factor? For the most recent year, the development factor does almost all the work. Ask the actuary to show what the ultimate would be if the factor moved up or down by a reasonable amount. This is the fastest way to understand how much uncertainty the estimate carries.
5. Did you run a method and then reject it? If so, why? The methods an actuary chose not to use are as informative as the methods they did use. A rejected method often points to a data issue or an assumption violation that the buyer should know about.
What to require in documentation
Your actuarial report should contain, at minimum, the following for each accident year:
- The method or methods considered, with the selected method clearly identified.
- The selected development factors, with the averaging basis (all-year, five-year, volume-weighted) and any exclusions.
- The expected claim ratio, if BF, Cape Cod, or expected claims was used, with its derivation.
- A comparison exhibit showing the indicated ultimate from at least two methods side by side.
- A narrative explanation of any accident year where the selected ultimate differs materially from the chain ladder indication.
If the report does not contain these items, you are not receiving a complete analysis. You are receiving a number. The point estimate vs. range discussion explains why a single number without context is the least useful form a reserve estimate can take.
Further reading
For the foundational concept of IBNR that every method is estimating, see IBNR, Explained Without the Jargon. For a detailed walkthrough of the triangle that feeds most of these methods, see How to Read a Loss Development Triangle. For diagnostic signals that something in the underlying data has changed, see What’s Actually Driving Your IBNR Higher? and Five Leading Indicators of Adverse Reserve Development. For the point-vs.-range question that follows any method selection, see Point Estimate vs. Range.