IBNR methods

At any balance sheet date an insurer owes claims it does not yet know about. A collision on December 30 is reported in January; a professional liability suit can arrive years after the act that caused it. On top of those come the development of claims already reported, whose case reserves move as information arrives. IBNR (incurred but not reported) estimates both: pure IBNR and the deficiency in case reserves, known in the literature as IBNER.

In Mexico, the LISF groups this concept into the reserve for claims incurred but not reported (SONR), part of the reserve for outstanding obligations, together with allocated loss adjustment expenses. The legal framework, the LISF articles and the CUSF chapters are covered in the technical reserves guide; this page focuses on methods.

No method is right on its own. Professional practice, as set out in the Friedland text that the CAS distributes free of charge, is to project with several methods, understand why they differ and select an estimate with documented judgment.

The input is the development triangle. Rows are origin periods: accident year (most common in P&C), underwriting year (useful in reinsurance and when coverage extends over time) or report year (for claims-made policies). Columns are development ages and cells hold cumulative amounts: paid, incurred (paid plus case reserves) or counts of reported and closed claims.

Before projecting, review diagnostics that reveal operational changes: the paid-to-incurred ratio by age (if it rises along recent diagonals, payments are faster or case reserves weaker), claim closure rates, the average case reserve per open claim adjusted for inflation, and average severity. A shift along a diagonal rather than a row points to an internal change (systems, reserving policy, adjusters) rather than to the risk itself.

Homogeneity matters too: separate lines and coverages with different patterns, isolate large or catastrophe losses that distort factors, decide whether to work gross or net of reinsurance, and treat salvage and recoveries consistently. A well built triangle is worth more than a sophisticated method.

With the triangle ready, compute individual age-to-age factors and choose an average for each column. The volume weighted average is the chain ladder estimator and gives more weight to large years; the simple average treats every year equally; the medial average drops the high and low to limit outliers; averages of the latest three or five years respond to recent changes at the cost of more volatility. The final selection is usually a judgment informed by all of them.

When the triangle does not reach full development, a tail factor is needed. Richard Sherman proposed in 1984 fitting the inverse power curve, in which the excess of the factor over one decays as a power of age; exponential decay gives shorter tails. Other options are the incurred-to-paid ratio at the most mature age, industry benchmarks or Clark's growth curves. The tail can be a material share of the reserve in liability and workers' compensation.

The classic methods differ in how much they trust observed experience versus an a priori expectation. From least to most weight on reported losses: expected loss ratio, Cape Cod and Bornhuetter-Ferguson, Benktander and chain ladder.

A point estimate says nothing about how wrong it might be. Stochastic models quantify uncertainty, which the LISF requires to be reflected in the risk margin and the capital requirement, and IFRS 17 in the risk adjustment for non-financial risk.

Triangles aggregate and lose information: the injury type, attorney, region or adjuster on each claim. Individual claim models project each claim from its own features. Mario Wüthrich published in 2018, in the Scandinavian Actuarial Journal, a regression tree approach to individual claims reserving, and Kevin Kuo presented DeepTriangle in 2019, a recurrent neural network trained on many industry triangles at once.

These methods promise more accuracy when data is rich and stable, but they require model governance, explainability for regulators and auditors, and validation against classic methods. In practice they coexist: machine learning helps to segment, detect shifts or estimate large losses, and the triangle remains the common language. More context in the article on predictive analytics in reserving and in Actuar.IA.

The choice depends on maturity, data stability and available information. This matrix summarizes common practice; in every case run at least two methods and explain the difference.

Under the LISF, IBNR is part of the reserve for outstanding obligations and is valued as a best estimate plus a risk margin. Article 219 requires the actuarial method for this reserve to be registered with the CNSF; Title 5 of the CUSF governs its constitution, method registration and the statutory method the Commission assigns when a company's own method does not adequately reflect its obligations, and Annex 5.3.2 classifies triangles by origin and development year. Adequacy is reviewed in the annual actuarial opinion under Annex 23.3.1.

Companies reporting to a parent under IFRS 17 also estimate the liability for incurred claims with their own risk adjustment for non-financial risk. Each provision, with links to the CUSF, is covered in technical reserves in Mexico and in IFRS 17.

Two free libraries implement nearly everything described here. In R, the ChainLadder package includes chain ladder, Mack, Munich Chain Ladder, bootstrap and Clark models. In Python, chainladder-python, maintained under the CAS organization, follows a scikit-learn style interface and reproduces the examples from the Friedland text. More resources in actuarial science in R and Python.

The founding IBNR papers appeared in actuarial journals that are still active: the CAS Proceedings and Variance, the IAA's ASTIN Bulletin, the British Actuarial Journal and the Scandinavian Actuarial Journal. See our directory of actuarial journals for recent issues, the essential books library and the guide to where to buy actuarial books.