Reserving Data Organization

Study guides: Exam 5, Exam 7, Exam GI-101

Reserving Data Organization is the grouping of claim and exposure data into cohorts for estimating unpaid claims. Friedland's framing differs from ratemaking's: the cohort must be a set of claims whose emergence pattern is stable enough to project forward, and it must be segmented so that each triangle is internally consistent.

\text{Unpaid} = \text{Ultimate} - \text{Paid to date}

\text{IBNR} = \text{Ultimate} - \text{Reported to date}

• Accident Year is the default reserving basis for direct business: claims grouped by occurrence date produce a Development Triangle whose rows share an exposure period and whose columns share a maturity.
• Policy Year and Underwriting Year are used where the contract, not the calendar, defines the cohort — reinsurance and large-deductible programs — at the cost of a longer, more leveraged development pattern.
• Report Year is the basis actuaries often prefer for claims-made business: a report year contains no pure IBNR, and its claim count is fixed at the close of the year.
• Calendar Year is never a reserving cohort. Its diagonal is the data — a calendar year is one diagonal of every triangle — and a diagonal effect (a reserve strengthening, a settlement push, a change in inflation) is a distortion to be diagnosed, not a cohort to be projected.

Beyond the time basis, Friedland's segmentation requirements:

• Split into groups that balance Homogeneity against Credibility — by line, coverage, tail length, and by claim type where settlement patterns genuinely differ.
• Keep gross, ceded and net triangles separate rather than netting inside the data; the ceded pattern differs from the gross one because reinsurance attaches to large, slow claims.
• Handle recoveries consistently: decide whether salvage and subrogation and deductible recoveries are netted in the triangle or estimated separately, and apply the same treatment to every year.
• Keep counts alongside dollars. Paid, reported, closed and open claim counts (Claim Count Triangle) are what make the dollar triangles diagnosable.

Segmenting a Book Before Building Triangles A regional insurer writes personal auto: bodily injury liability, property damage liability, collision, and comprehensive. Total annual premium is \$60{,}000{,}000, split 35/15/35/15. Physical damage claims close within months; BI claims run several years.

How should the reserving data be organized?

Answer Separate triangles for BI, PD, and physical damage (collision and comprehensive together or apart). Combining them would average a multi-year liability pattern with an essentially immediate property pattern, producing development factors that fit neither.

Working through the segmentation criteria:

• Homogeneity — BI is long-tail, high severity, litigated; comprehensive is short-tail, high frequency, low severity. Different patterns, so different triangles.
• Credibility — at \$21{,}000{,}000 of BI premium there is ample volume for its own triangle; splitting comprehensive further by peril would thin it out for little gain.
• Practicality — comprehensive is dominated by catastrophe-driven diagonals (hail), which argues for pulling catastrophe claims out and reserving them separately whatever the segmentation.

All four segments stay on an accident year basis so that the results aggregate and reconcile to the financial statements.

Why the Calendar Year Is a Diagnostic, Not a Cohort A reported-loss triangle shows the following age-to-age factors. The most recent diagonal (valuation 12/31/2024) is bolded.

AY	12–24	24–36	36–48
2021	1.55	1.20	1.14
2022	1.52	1.26
2023	1.61

Historical averages excluding the latest diagonal are 1.53, 1.20 and 1.08.

What does the pattern indicate, and how should the actuary respond?

Answer Every factor on the 12/31/2024 diagonal is above its historical average, at every maturity. That is a calendar year effect: something happened in 2024 that raised reported losses across all accident years simultaneously — most commonly a strengthening of case reserve adequacy, but a legal or inflationary shock does the same thing.

The wrong response is to average the elevated factors into the selections, which would apply a one-time level shift to every future year as if it were an ongoing pattern.

The right response is to diagnose first: check average case outstanding by maturity and the closure rate for a corresponding shift, ask claims management what changed (Friedland Ch. 4), and if case adequacy has genuinely increased, restate the historical triangle with the Berquist-Sherman case-adequacy adjustment before selecting factors.