# Loss reserve studies for workers' compensation and liability self-insurance

Canonical: https://finbryn.com/us/services/actuarial-services/loss-reserve-studies

Finbryn provides loss reserve study support for employers and captives that self-insure workers' compensation, general liability and auto, running chain-ladder, Bornhuetter-Ferguson and expected loss ratio methods on your claims triangles, with ranges and funding levels, for review and signature by a credentialed signing actuary.

A reserve study answers one question: how much of what the program has already incurred is still unpaid? For a self-insurance program or a [captive](/services/insurance-accounting-support/captive-rrg-accounting-support), that unpaid amount is a liability on the financial statements and the basis for next year's funding. Workers' compensation, general liability and auto claims take years to close, so the answer is an estimate built from the program's own claims history, and a range matters as much as the point.

We start from loss runs: claims by accident year with paid losses, case reserves and, where tracked, allocated expenses and recoveries, at each valuation date. We organize them into development triangles by program and line, then apply standard methods side by side: paid and incurred chain-ladder, Bornhuetter-Ferguson, and expected loss ratio. The workpapers show every factor, every selection and the reason for it.

The output is a set of unpaid loss estimates by accident year, a range around the central estimate with the drivers behind it, a funding projection for the next program year and accrual support for the financial statements. Where a captive's domicile requires a statement of actuarial opinion on reserves, the opinion is a separate document that only a qualified actuary signs.

Finbryn prepares the data work, triangles, projections and workpapers. [Hesham Khan](/about) is Finbryn's signing actuary: he reviews the methods and selections and signs the reserve report. Any statement of actuarial opinion is signed by the actuary the engagement letter names, who must meet the applicable qualification standard, and your auditor reviews the result. This is reserve support for operating self-insurance programs and captives. We do not market micro-captive or 831(b) structures.

What you get: Loss development triangles by program and accident year; Unpaid loss estimates from more than one method, with the selection explained; A range around the central estimate and the drivers behind it; Funding and budget projections for the next program year; Accrual support for the financial statements

Software we work in: Microsoft Excel, Python, R

How filing works: We prepare the return and the working papers. A credentialed signer or licensed partner signs and files it, or you file it yourself.

## What does a loss reserve study cover for workers' compensation, liability and auto programs?

A loss reserve study estimates the unpaid cost of claims that have already occurred, for each line and accident year, and usually the loss adjustment expense that goes with them. This page covers workers' compensation, general liability and automobile liability, which develop at different speeds: the CAS text says short-tail lines such as auto physical damage are usually valued within one or two years, while workers' compensation and general liability can take many years, sometimes decades (Friedland, Chapter 1).

Unpaid loss means case reserves on open claims plus an estimate for claims not yet reported plus further development on known claims. The study separates paid-to-date from the estimate of ultimate, so the sponsor sees what has been paid, what the claims adjusters have reserved, and what the actuarial method adds on top.

For captives, the same work supports the reserves held by the captive and the financial statement liability. ASOP No. 36 (effective October 1, 2024) covers statements of actuarial opinion on loss and loss adjustment expense reserves and names self-insurers and risk-sharing pools among the entities it applies to. Our role is the support; the opinion belongs to the actuary who signs it.

## How does the chain-ladder method estimate unpaid losses?

Chain-ladder projects each accident year to ultimate by multiplying its latest cumulative amount by a cumulative development factor built from the program's own age-to-age history. The CAS text calls it the development technique and lays out seven steps: compile the triangle, compute age-to-age factors, average them, select factors, select a tail, compute cumulative factors and project ultimate (Friedland, Chapter 7).

All figures below are Illustrative, in $000, made up and not an estimate for any entity. This is an illustration, not an actuarial opinion. Valuation date is December 31, 2026, and the tail factor past 60 months is 1.000.

Cumulative paid losses by accident year and age in months:

| Accident year | 12 | 24 | 36 | 48 | 60 |
| --- | ---: | ---: | ---: | ---: | ---: |
| 2022 | 1,000 | 1,550 | 1,980 | 2,200 | 2,300 |
| 2023 | 1,100 | 1,800 | 2,200 | 2,400 | |
| 2024 | 1,000 | 1,650 | 2,000 | | |
| 2025 | 1,100 | 1,760 | | | |
| 2026 | 1,100 | | | | |

Age-to-age factors, the all-year simple average, the selected factor and the cumulative development factor to ultimate:

| Accident year | 12-24 | 24-36 | 36-48 | 48-60 | 60-ult |
| --- | ---: | ---: | ---: | ---: | ---: |
| 2022 | 1.550 | 1.277 | 1.111 | 1.045 | |
| 2023 | 1.636 | 1.222 | 1.091 | | |
| 2024 | 1.650 | 1.212 | | | |
| 2025 | 1.600 | | | | |
| Simple average | 1.609 | 1.237 | 1.101 | 1.045 | |
| Selected | 1.600 | 1.250 | 1.100 | 1.050 | 1.000 |
| Cumulative to ultimate | 2.310 | 1.444 | 1.155 | 1.050 | 1.000 |

Factors are rounded to three decimals for display. The selected factors are judgment, set close to the averages. The cumulative factor at 12 months is 1.600 x 1.250 x 1.100 x 1.050 x 1.000 = 2.310; the 24-month factor is 1.25 x 1.1 x 1.05 = 1.44375, shown as 1.444.

The diagram shows the paid triangle, with the latest diagonal being the paid-to-date column.

Diagram: Illustrative cumulative paid loss triangle, $000. Cumulative paid losses for accident years 2022 to 2026 at 12, 24, 36, 48 and 60 months of development, valuation date December 31, 2026. Made-up numbers, lower-right cells empty. (Illustrative.)

## What do the factors give, and how do paid and incurred chain-ladder differ?

Multiplying each accident year's paid-to-date by its cumulative factor gives ultimate losses, and ultimate less paid is the unpaid estimate. Using the cumulative factors above, in $000, still Illustrative:

| Accident year | Paid to date | Cumulative factor | Ultimate | Unpaid |
| --- | ---: | ---: | ---: | ---: |
| 2022 | 2,300 | 1.00000 | 2,300 | 0 |
| 2023 | 2,400 | 1.05000 | 2,520 | 120 |
| 2024 | 2,000 | 1.15500 | 2,310 | 310 |
| 2025 | 1,760 | 1.44375 | 2,541 | 781 |
| 2026 | 1,100 | 2.31000 | 2,541 | 1,441 |
| Total | 9,560 | | 12,212 | 2,652 |

The totals check: 12,212 less 9,560 paid is 2,652.

Paid chain-ladder develops payments. Incurred chain-ladder develops payments plus case reserves. The paid method does not depend on adjusters' reserving, but its factors are large at early ages. The incurred method starts closer to ultimate, but it breaks down if reserving practice changes. Friedland notes that where cumulative factors are high, each dollar is multiplied by that factor and one large claim can distort the newest years, so actuaries then often look for alternative techniques. We run both on the same triangle dimensions; a gap between them points to a data or claim handling change, and the memo says which explanation we tested.

## When do Bornhuetter-Ferguson and expected loss ratio methods beat chain-ladder?

Bornhuetter-Ferguson and the expected loss ratio method beat chain-ladder for recent, immature accident years where the cumulative factor is large and the claims experience so far is thin. Expected loss ratio ignores the claims experience and takes premium, payroll or another exposure measure times an expected loss ratio. Bornhuetter-Ferguson blends the two: actual paid to date plus an expected unpaid share, where the expected unpaid share is the a priori expected ultimate times (1 minus 1 / cumulative factor). Friedland covers these in Chapters 8 and 9.

Illustration for accident year 2026 using the 12-month cumulative factor of 2.310 from above, in $000. Exposure of 3,300 with an expected loss ratio of 70% gives an expected ultimate of 2,310.

| Method for AY 2026 | Ultimate | Unpaid |
| --- | ---: | ---: |
| Paid chain-ladder: 1,100 x 2.310 | 2,541 | 1,441 |
| Bornhuetter-Ferguson: 1,100 + 2,310 x (1 - 1/2.310) | 2,410 | 1,310 |
| Expected loss ratio: 3,300 x 70% | 2,310 | 1,210 |

Check: 2,310 x (1 - 1/2.310) = 2,310 - 1,000 = 1,310, so the Bornhuetter-Ferguson ultimate is 1,100 + 1,310 = 2,410. The three methods span 1,210 to 1,441 for the same year, a spread of 231, which is why a study never rests on one method for the newest years.

## How are methods selected, ranges set, and funding chosen at a confidence level?

The signing actuary selects among methods by accident year, weighing how mature the year is, how stable the data and claim handling have been, and how reliable the exposure base is. Older, mature years lean on chain-ladder. The newest years lean on Bornhuetter-Ferguson or expected loss ratio. The selected unpaid for the illustration uses chain-ladder for 2022 to 2025 and Bornhuetter-Ferguson for 2026: 0 + 120 + 310 + 781 + 1,310 = 2,521, in $000.

A range exists because the central estimate is one point in a distribution of outcomes. Ranges can be built from the spread across reasonable methods, from the variability in the age-to-age factors, or from a stochastic model. Which is used, and what drives the width, such as claim count, severity volatility, large claim exposure or a change in claims administration, goes in the memo.

Funding at a confidence level means setting the program's funding or accrual at a chosen percentile of the estimated distribution of ultimate unpaid losses instead of at the expected value. A 75% confidence level means the funded amount is estimated to be enough about three times in four. Public entities, captives and some boards set a policy for this. We prepare the percentile calculations for the signing actuary's review, and the policy choice stays with the sponsor.

## How does a reserve study run, from loss runs to signed results?

A reserve study runs in six steps: the client supplies loss runs, we reconcile them and build triangles, we run the methods, we prepare selections and a range, the credentialed signing actuary reviews and signs, and the auditor and sponsor use the result. The diagram shows the flow, with the signing step marked in its own color.

Loss runs come from the third-party administrator or the claims system, with valuation dates that line up and a stated treatment of recoveries, subrogation and large claims. We reconcile claim counts and paid totals to the previous study and to the general ledger before any factor is computed. Mismatches are listed and sent back for explanation.

After the methods run, the memo sets out the method for each year, the selected unpaid, the range and the funding projection for the next program year. The signing actuary reviews the data, methods and assumptions, and signs whatever statement the situation requires. The auditor then receives the signed result with the supporting workpapers for the financial statement accrual. Studies are usually refreshed once a year at the same valuation date, which keeps the prior study as the benchmark for the next one.

Diagram: How a loss reserve study runs. Six steps from the client's loss runs to the signing actuary's review and the auditor's use of the result.

## What does a loss reserve study cost?

The fee depends on the number of programs and lines, the number of accident years in the history, the quality and format of the loss runs, how often the study is refreshed and whether a statement of actuarial opinion is required. A single line with five years of clean loss runs is a smaller engagement than three lines, a captive and a prior study that needs reconciling.

Data quality often drives the fee. Loss runs that mix valuation dates, omit recoveries or change layout between years take longer to rebuild before any analysis begins. Frequency matters too: an annual study refresh costs less than a first study, because the triangles and prior selections carry forward.

Public procurement records show how bodies buy this work, but the ones we found are small updates to older agreements or do not state a comparable full-study fee, so this page does not publish a range. Finbryn confirms scope and fee in writing before work starts, and the quote names who signs.

## The process

1. **Agree scope and the signing actuary**: Lines, programs, valuation date and the signing actuary named in the engagement letter.

2. **Collect loss runs**: Claims by accident year with paid, case reserves, recoveries and any allocated expense, at each valuation date.

3. **Reconcile and build triangles**: Tie counts and totals to the ledger and the prior study, then build paid and incurred triangles by line.

4. **Run the methods**: Paid and incurred chain-ladder, Bornhuetter-Ferguson and expected loss ratio, with every factor shown.

5. **Prepare the selection, range and funding view**: Unpaid by accident year, the drivers of uncertainty, and funding at the confidence levels the sponsor chooses.

6. **Signing actuary reviews and signs**: The credentialed actuary reviews methods, selections and any opinion, and signs what the situation requires.

7. **Auditor review**: Your auditor receives the memo, workpapers and signed results to support the accrual.

## Common problems we fix

| The problem | How we fix it |
| --- | --- |
| Loss runs from different valuation dates are mixed in one triangle | We rebuild each diagonal from one valuation date per column and list every cell we had to adjust. |
| A new administrator changed how case reserves are set | We compare paid and incurred results; a gap between them is the first signal, and we document the test. |
| The newest year has one large claim and a huge development factor | We project that year with Bornhuetter-Ferguson or expected loss ratio and show the large claim separately. |
| The board wants one number, but the data supports a range | We give the central estimate, a range, the drivers, and the funding amount at each confidence level the board's policy names. |
| The captive's reserves and the parent's financial statements use different estimates | We reconcile both to one selected unpaid, with the difference explained line by line. |

## By the numbers

| Figure | What it means | Source |
| --- | --- | --- |
| Oct 1, 2024 | effective date of ASOP No. 36, covering statements of actuarial opinion on property/casualty loss and loss adjustment expense reserves, including for self-insurers | [actuarialstandardsboard.org/asops/asop-no-36-statements-of-actuarial-opinion-regarding-property-casualty-loss-loss-adjustment-expense-or-other-reserves](https://www.actuarialstandardsboard.org/asops/asop-no-36-statements-of-actuarial-opinion-regarding-property-casualty-loss-loss-adjustment-expense-or-other-reserves/) (2026-10-02) |
| 7 steps | in the CAS text's development (chain-ladder) technique, from the triangle to projected ultimate claims | [casact.org/sites/default/files/database/studynotes_friedland_estimating.pdf](https://www.casact.org/sites/default/files/database/studynotes_friedland_estimating.pdf) (2026-10-02) |

## Glossary

- **Accident year**: The year in which the loss occurred, regardless of when it was reported or paid.

- **Development triangle**: A table of cumulative paid or incurred losses by accident year and age, with the lower-right cells empty because those values have not happened.

- **Age-to-age factor**: The ratio of a year's cumulative amount at one age to the same year's amount at the previous age.

- **Cumulative development factor**: The product of the selected age-to-age factors and the tail from a given age to ultimate.

- **Tail factor**: The development expected beyond the oldest age in the triangle.

- **Chain-ladder**: A method that projects ultimate losses by multiplying the latest cumulative amount by the cumulative development factor. Friedland calls it the development technique.

- **Bornhuetter-Ferguson**: A method that adds actual paid or reported losses to an expected unpaid or unreported share of an a priori expected ultimate.

- **Expected loss ratio method**: A method that sets ultimate losses at an exposure base, such as premium or payroll, times an expected loss ratio.

- **Case reserve**: The claim adjuster's estimate of what remains to be paid on a known open claim.

- **Confidence level**: The probability, estimated from a distribution of outcomes, that the funded amount covers the ultimate unpaid losses.

## Frequently asked questions: Loss reserve studies for workers' compensation and liability self-insurance

**Q: How do you calculate loss reserves for a workers' compensation self-insurance program?**

A: Build development triangles from loss runs, compute age-to-age factors, select factors and a tail, and project each accident year to ultimate with chain-ladder. For recent years, add Bornhuetter-Ferguson and expected loss ratio. The CAS text Estimating Unpaid Claims Using Basic Techniques (opened 2026-10-02) sets out each method, and the signing actuary reviews the selections.

**Q: What is the difference between chain-ladder and Bornhuetter-Ferguson?**

A: Chain-ladder scales a year's actual losses by a development factor, so it follows the data but gets volatile for immature years. Bornhuetter-Ferguson adds actual losses to an expected unpaid share of an a priori estimate, so it moves less with one large claim. In the illustration on this page, they give unpaid of 1,441 and 1,310 for accident year 2026.

**Q: How accurate is a reserve estimate and why show a range?**

A: A reserve is an estimate of future payments, so the actual outcome will differ. A range shows how much, using the spread across methods, factor variability or a stochastic model, and names the drivers such as claim count and large claims. Funding policy can then refer to a confidence level instead of one number.

**Q: Can you help a captive with reserves?**

A: Yes, as reserve support: triangles, method runs, selections and workpapers for the signing actuary and your auditor. A statement of actuarial opinion, where the domicile requires one, is signed by the qualified actuary the engagement letter names. We do not market micro-captive or 831(b) programs.

**Q: What data do I need for a loss reserve study?**

A: Loss runs by accident year with paid losses, case reserves and recoveries at each valuation date, claim counts, and an exposure measure such as payroll or premium. Five or more accident years is the usual starting point. Send de-identified claim data; claimant names, Social Security numbers and medical details are not needed.

**Q: Who signs a reserve study and any opinion?**

A: Finbryn's signing actuary reviews and signs the reserve study. For any statement of actuarial opinion, the engagement letter names the signer, who must meet the applicable US standard; for opinions on property/casualty reserves, ASOP No. 36 (effective October 1, 2024) is the standard that applies. Finbryn prepares the workpapers and calculations.

**Q: What does a loss reserve study cost?**

A: The drivers are the number of programs and lines, the years of history, loss run quality, refresh frequency and whether an opinion is required. Finbryn confirms scope and fee in writing before work starts, and the written quote names who signs.

**Q: How do I choose a provider for a loss reserve study?**

A: Ask who signs and what US standard that person meets, which methods will be run and how the selection will be explained, whether you receive a range and the drivers behind it, how loss runs are reconciled, and whether your auditor can see the workpapers. Ask any provider for a sample triangle built on made-up numbers.

**Q: What actuarial work does a captive insurance program need?**

A: Captive domiciles commonly ask for an actuarial feasibility analysis with the license application and a reserve review each year, and requirements differ by domicile, so confirm with the regulator. We prepare the reserve workpapers; a credentialed actuary signs any opinion (ASOP No. 36, checked 2026-10-02). We do not market tax-driven captive structures.

Related services:
- [Captive and risk retention group accounting support](https://finbryn.com/us/services/insurance-accounting-support/captive-rrg-accounting-support)
- [Insurance rate making and pricing support](https://finbryn.com/us/services/actuarial-services/insurance-rate-making-pricing-support)
- [Self-funded health plan IBNR and COBRA rate support](https://finbryn.com/us/services/actuarial-services/self-funded-health-ibnr-cobra-rates)
- [White-label actuarial support for accounting firms and TPAs](https://finbryn.com/us/services/actuarial-services/white-label-actuarial-support)

Related guides:
- [IFRS 17 vs LDTI (ASC 944): Key Differences](https://finbryn.com/us/guides/ifrs-17-vs-ldti-asc-944)

## Sources

1. [Casualty Actuarial Society, Friedland, Estimating Unpaid Claims Using Basic Techniques (Version 3, 2010)](https://www.casact.org/sites/default/files/database/studynotes_friedland_estimating.pdf) (2026-10-02)
2. [Actuarial Standards Board, ASOP No. 36, Statements of Actuarial Opinion Regarding Property/Casualty Reserves](https://www.actuarialstandardsboard.org/asops/asop-no-36-statements-of-actuarial-opinion-regarding-property-casualty-loss-loss-adjustment-expense-or-other-reserves/) (2026-10-02)
3. [American Academy of Actuaries, US Qualification Standards (Appendix 1)](http://actuary.org/sites/default/files/2021-11/USQS_2021.pdf) (2026-10-02)

Reviewed October 2026

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