Claims provisions in liability insurance

The settlement delay for very large claims in liability insurance may extend to quite a few years; a delay often years in automobile third‐party liability is by no means an exception. The companies consequently have to set aside huge amounts as provisions for outstanding claims. As the total provision may attain 100 times the underwriting profit, an underestimation of this provision of a few per cent could mean short‐term bankruptcy for the company. A precise forecast of those outstanding liabilities is therefore of crucial importance Owing to the special nature of the information set (a triangular array of cumulative payments, called the‘run‐off triangle’), actuaries have in the past neglected the time series analysis approach and devised their own forecasting models. Those methods are reviewed, and illustrated by a real‐life example. Two new autoregressive methods are proposed.