Excess Liability Reserve with Sparse Large-Loss Experience
A specialty insurer writes occurrence-based excess liability over a $1M self-insured retention, with a $10M per-occurrence limit. The book began in 2019, and cumulative earned premium through 2024 is $70M. At year-end 2024, the reported loss triangle has only three claims above $5M, and one construction-defect claim from accident year 2021 was just increased from $4M to $9M. Paid losses to date are $11M and case reserves are $19M. The largest case is reserved at the $10M limit. The actuarial team has a ground-up expected loss ratio of 65% from an exposure-rating model, but development factors are based on only four diagonals and are volatile. Reinsurance is in place above $5M per occurrence, but the reinsurer disputes the 2021 claim's coverage. Management wants a point estimate and a range for the 2024 IBNR.
1. Evaluate whether a chain-ladder development method is credible for this book and propose an alternative or complementary approach.
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Chain ladder is not credible as the primary method. Four diagonals are too few for a long-tailed excess liability book, and the triangle is dominated by a handful of large claims. The 2021 construction-defect claim moving from $4M to $9M is an idiosyncratic case-reserve development, not a stable development pattern. Development factors will swing based on whether one large claim settles, closes, or is re-reserved. I would use the expected loss ratio method or Bornhuetter-Ferguson as the primary indication, because it anchors the estimate to exposure and expected loss ratio rather than to unstable historical development. I would supplement it with a frequency-severity analysis of large claims and a separate individual large-loss review. The chain-ladder result can be shown as a diagnostic, but it should receive low credibility weight.
2. Describe how you would treat the disputed reinsurance claim and the limit-capped case reserve in the reserve estimate.
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The gross reserve should not be reduced because the reinsurer disputes coverage. The insurer remains liable to the policyholder, so the gross case reserve for the 2021 claim must reflect the $9M estimate unless there is a documented legal basis to reduce it. Any ceded recoverable should be recognized separately only if coverage is probable and the reinsurer is collectible; given the dispute, I would set the ceded asset at zero or apply a substantial haircut, and disclose the contingency. The limit-capped case at $10M should be tested for whether the limit is truly exhausted and whether defense costs or multiple claimants could erode the limit differently. For IBNR, I would treat large claims separately from the attritional book and avoid letting a single limit-capped claim drive the development factors.
3. Provide a reasoned point estimate and range for the 2024 IBNR given the data, stating your assumptions.
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Expected ultimate is 65% x $70M = $45.5M. Reported losses are $11M paid plus $19M case = $30M, or 66% of expected ultimate. If I assume 70% reported-to-ultimate, BF IBNR is 30% x $45.5M = $13.65M. If large-loss development suggests only 60% reported, IBNR rises to 40% x $45.5M = $18.2M; if reporting is faster at 75%, IBNR falls to $11.4M. A defensible point estimate is about $14M, with a range of $11M to $18M. The range should widen for the disputed reinsurance and for uncertainty in the construction-defect claim. The point estimate is gross of reinsurance; any ceded benefit is a separate collectibility judgment.