developing losses to ultimate for pricing

When you price next year's policies from a recent year's claims, there is a problem hiding in the data: a recent accident year is not finished. Some claims from that year have not even been reported yet, and many that are reported are not yet fully paid because lawsuits, medical treatment, or repairs are still ongoing. The losses you can see today understate what the year will eventually cost. Developing losses to ultimate is the step that estimates that final, fully-mature figure.

The tool is the loss development triangle. You arrange historical accident years down the side and 'months of maturity' across the top, and watch how the recorded losses for each year grow as time passes. From these you estimate age-to-age factors — for instance, losses tend to grow 1.20 times from 12 to 24 months, then 1.07 times from 24 to 36, and so on — and chain them together into a loss development factor that scales an immature year up to ultimate. If a recent accident year shows 5 million dollars at 12 months and the 12-to-ultimate factor is 1.50, the estimated ultimate is 7.5 million. The same chain-ladder machinery used in reserving is borrowed here, but for a forward-looking purpose.

Development matters in pricing because using raw immature losses would systematically underprice — the more recent the data, the bigger the understatement. It is also where pricing and reserving meet: both lean on the same triangles, but pricing then layers trend on top to project to the future, whereas reserving stops at estimating today's liability. A caution: long-tailed lines like liability are far more sensitive to the chosen factors than short-tailed lines like auto physical damage, and small changes in late-age tail factors can swing the indicated rate noticeably.