Actuarial Notes

Incurred Losses

Study guide: Exam 5

Incurred Losses — more precisely reported losses — are cumulative payments plus case outstanding on known claims at a valuation date. They are the insurer's current estimate of what the reported claims will ultimately cost, and they exclude IBNR.

\text{Reported (Incurred)} = \text{Paid} + \text{Case Reserves}

\text{Ultimate} = \text{Reported} + \text{IBNR}

  • The vocabulary matters on the exam. "Incurred" in a calendar year context (paid + \Delta case + \Delta IBNR) is a different quantity from "reported" in an accident year triangle (paid + case). Friedland uses reported for the triangle to avoid the ambiguity.
  • Reported triangles emerge faster and more smoothly than paid ones, because a case reserve is set as soon as a claim is known. Reported development factors are therefore smaller and the chain ladder is less leveraged.
  • The cost is exposure to adjuster judgment. Reported development mixes genuine emergence with IBNER — re-estimation of known claims — so any systematic change in case adequacy corrupts the historical factors. A single strengthening initiative shows up as an elevated diagonal across every accident year at once.
  • Reported losses can develop downward. Conservative initial reserving, salvage and subrogation recoveries, and claims closing below their case reserve all produce age-to-age factors under 1.000; capping factors at 1.000 on principle is a standard error.
  • At ultimate, case reserves run off to zero and reported losses converge to paid. The gap between reported and ultimate at any maturity is IBNR.

Reported Development and IBNR Accident year 2022 has reported losses of \$800{,}000 at 24 months. The selected cumulative reported factor to ultimate is 1.35.

Estimate ultimate losses and IBNR, and state what the IBNR consists of.

Answer

\begin{align*}
\text{Ultimate} &= \$800{,}000 \times 1.35 \\
&= \$1{,}080{,}000 \\[4pt]
\text{IBNR} &= \$1{,}080{,}000 - \$800{,}000 \\
&= \$280{,}000
\end{align*}

That \$280{,}000 is broad IBNR — two components in one number:

  • Pure IBNR: claims that occurred in 2022 and are still unknown to the insurer at 24 months.
  • IBNER: expected upward development on the claims already in the \$800{,}000, as case reserves move toward settlement values.

Splitting the two requires a claim count triangle — develop counts to ultimate, subtract reported counts, and value the unreported claims at an expected severity. The split matters when reporting patterns and case adequacy are moving in different directions.

A Case Reserve Strengthening in the Triangle Reported age-to-age factors for a liability line:

AY 12–24 24–36 36–48
2020 1.48 1.19 1.07
2021 1.50 1.18 1.15
2022 1.47 1.31
2023 1.66

Average case outstanding per open claim rose 28\% during 2023 across all accident years. What happened, and what should the actuary do?

Answer The bolded figures form the latest diagonal — the year ending 12/31/2023 — and every one of them is above its column's history. Combined with the jump in average case outstanding, this is a case reserve strengthening, not a change in the underlying loss cost.

Selecting factors that include the elevated diagonal would apply a one-time level shift as if it were an ongoing pattern, over-stating every future year's development.

Two defensible responses:

  1. Restate the triangle with the Berquist-Sherman case-adequacy adjustment: trend historical average case outstanding up to the current level, rebuild the reported triangle, and select factors from the restated history.
  2. Lean on paid data, which is unaffected by case adequacy — provided the settlement rate has been stable, which must be checked separately.

Doing neither, and simply excluding the latest diagonal, avoids the distortion in the factors but leaves the diagonal itself in the data — the strengthened reserves are still on the books, so the ultimate estimate must acknowledge them.