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Individual claims reserving

Reserving that models each claim, from report to closure, instead of projecting the aggregated sums of a triangle, so as to keep the information the claim file carries.

Definition

Katrien Antonio and Richard Plat published a micro-level reserving model in the Scandinavian Actuarial Journal in 2014, in which each claim is followed from occurrence to closure. Each piece is modeled separately: a reporting delay, then a sequence of events (payment, payment with closure, closure without payment), then amounts. The aggregated triangle throws all of that away. It sees one sum per cell, while the file knows the type of injury, whether counsel has been retained, the expected date of medical consolidation, the handler working it. Mario Wüthrich took the idea further in 2018 in the same journal, under the title "Machine learning in individual claims reserving." He handed regression trees the job of predicting each claim's payments from its features. The clearest gain is on changes in mix. When the share of bodily injury files rises, chain ladder applies patterns calibrated on the old blend, while the individual model projects each claim for what it is. The limits are familiar to teams that have tried it: you need clean, dated claims-handling histories, statuses and reserve movements included, which few claims systems keep over fifteen years. And validation is still done against the triangle, for lack of anything better. An auditor reads a development factor in a minute; a model with several hundred parameters takes far longer. Hence its frequent use as a check method alongside the triangle. Not to be confused with the case reserve, which is the handler's estimate and not a statistical model, or with stochastic reserving, which is usually aggregated.

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Individual claims reserving: Actuarial science glossary illustration, AlgoPolis
Example

Constructed example: a liability book has 400 open claims at the closing date. The individual model expects 2,000 euros of remaining payments per property damage file and 18,000 euros per bodily injury file. The mix has moved: 300 property and 100 injury files, so 600,000 + 1,800,000 = 2.4 million euros. The triangle carries the historical blend of 90% property, the equivalent of 360 and 40 files: 720,000 + 720,000 = 1.44 million euros. The 960,000 euro gap comes from the change in mix alone.

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Related terms
Also known as

micro-level reserving, individual loss reserving, claim-level reserving, micro-level stochastic reserving

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