Motor Liability Reserve Adequacy with Thin Development Data

The chain-ladder method assumes stable development patterns and that past development is predictive. That is questionable here. The latest two accident years have only about 60 reported claims each, so development factors are highly volatile and could be distorted by a single large claim. The 7% case-reserve strengthening indicates that earlier case estimates were inadequate, which may also inflate observed development in the latest diagonal and make the chain-ladder understate or overstate the tail depending on direction. The 18% severity increase is not necessarily a change in development; it may be inflation, mix or injury-award trends, so it should be handled explicitly rather than left in the factors.

I would: (i) separate large claims and assess them individually; (ii) test chain-ladder against Bornhuetter–Ferguson and frequency–severity methods, using external benchmarks for inflation and settlement rates; (iii) adjust historical payments to a common cost level and consider future inflation; (iv) use a range of development patterns, not a single factor, and give weight to methods that are less dependent on immature data; (v) review the tail for injury claims beyond the triangle; and (vi) document expert judgement. The result should be a probability-weighted central estimate, not a mechanically selected chain-ladder result.

Under Solvency II the best estimate should be the probability-weighted expected value of future cash flows, with no deliberate margin. The risk margin is a separate amount to cover the cost of holding required capital, calculated using a cost-of-capital approach over the run-off. Adding a flat 5% to the central estimate is not a substitute for either: it is arbitrary, does not reflect the shape of the risk, and may be double counting if the best estimate already includes a prudent view.

I would set the best estimate from the weighted methods, then quantify uncertainty using stochastic reserving or scenario analysis. The risk margin should reflect the capital needed to support reserve risk over the run-off, allowing for diversification and reinsurance. The 70% quota share reduces net reserves and recoveries should be assessed for credit risk. Discounting should use the relevant risk-free term structure. I would present a central estimate with a range and explain that the 5% margin is neither transparent nor risk-based; if the board wants prudence, it should be an explicit capital buffer or a stated confidence level, not an opaque loading.

The board needs a clear central estimate, a range and the drivers of uncertainty, not just a single number. I would present: the recommended best estimate and the risk margin separately; a sensitivity table showing the effect of the 18% severity trend, a further 5% case-reserve strengthening, and alternative development patterns; the probability of deterioration; and the net impact after the 70% quota share and reinsurance recoveries. I would explain in plain language that the latest accident years are thin and that the 5% margin is not a risk measure. Decision-useful information includes the impact on statutory surplus, Solvency II own funds and SCR coverage, dividend capacity, and management actions if reserves develop adversely. I would also state monitoring triggers, such as quarterly claim-count and average-cost thresholds, and the governance route for changing the estimate. The aim is to make the trade-off between prudence and capital strain explicit, so the board can choose a confidence level rather than accept an unexplained loading.