Actuarial Notes

Gross Losses

Study guide: Exam 5

Gross Losses are losses before any cessions or recoveries are removed — the full amount of claim cost arising on the business the insurer wrote. Gross is the base from which ceded, recovery and net figures are derived.

\text{Gross} = \text{Net} + \text{Ceded} + \text{Other Recoveries}

\text{Gross Ultimate} = \text{Gross Reported} \times \text{CDF}^{\text{gross}}

  • "Gross" needs a qualifier. It most often means gross of reinsurance, but a figure can also be gross or net of salvage and subrogation, of deductible recoveries, and of ULAE. Every comparison must confirm which recoveries the gross figure excludes; the syllabus and the Annual Statement use the term in different senses.
  • Reserve analysis is normally run on gross data first: it is the largest and most homogeneous dataset, it is unaffected by changes in reinsurance structure, and the ceded and net figures follow from it.
  • Gross and ceded develop on different patterns — excess cessions attach only to large, slow claims — so ceded cannot be scaled from gross except under quota share. This is why net is derived as gross minus ceded rather than developed directly.
  • Gross data is also what survives a change of programme. When the treaty changes, the ceded and net histories break; the gross history does not, and it can be re-ceded under the new terms.
  • For ratemaking, whether to work gross or net depends on how the reinsurance cost is provided for — see Net of Reinsurance.

Reconciling Gross, Ceded and Net AY 2024: net retained losses \$800{,}000; excess-of-loss reinsurance recoverable \$300{,}000; salvage and subrogation recovered \$50{,}000.

What are gross losses?

Answer

\begin{align*}
\text{Gross} &= \$800{,}000 + \$300{,}000 + \$50{,}000 \\
&= \$1{,}150{,}000
\end{align*}

The insurer's policyholders were paid \$1{,}150{,}000; the insurer itself bore \$800{,}000 of it. Note that this figure is gross of both reinsurance and S&S — a "gross of reinsurance, net of S&S" figure would be \$1{,}100{,}000, and the two are quoted interchangeably often enough that the basis must be stated.

Why the Gross Triangle Survives a Treaty Change An insurer raised its per-occurrence retention from \$250{,}000 to \$1{,}000{,}000 effective 1/1/2022. Its analyst proposes developing the net triangle, on the grounds that net is what the company retains.

Evaluate.

Answer The net triangle contains two incompatible regimes: through AY 2021 it is net of a \$250K retention, from AY 2022 net of \$1M. Net losses jump upward at the break for a reason that has nothing to do with claim cost, and no development factor selected across that boundary describes either regime.

The gross triangle is unaffected — gross losses are what they are regardless of who ultimately pays them — so it can be developed with a consistent history and the full ten years of data.

The sound procedure is therefore:

  1. Develop gross to ultimate on the unbroken history.
  2. Estimate ceded separately by applying the current treaty terms to the projected gross large-claim distribution (Reinsurance Recovery).
  3. Derive net as the difference.

This is the general reason the gross basis is the analytical starting point: it is the only one of the three that is invariant to the insurer's own risk-transfer decisions.