Run off triangle and its use

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ActuaryJobs
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26 Jul 2018, 13:41

When a claim event occurs there will be some time before it is reported or notified to the insurer - this is known as a claim delay. The insurer will incur numerous claims in a calendar year, and each of those claims will have a claim delay. The run off triangles are used to estimate how much or how many claims have been incurred in a reporting period (eg financial year) but are not yet reported and a reserve is held for this. It's called an IBNR - incurred but not reported reserve. 

Simplified example: Consider a life insurer with 10 policyholders at 1 Jan 2016 - assume no joiners, no lapsing, no policyholder changes up to December 2016 - when 3 people die in mid month. 1 claim is notified to the insurer in December ($20 000). 1 is notified in early January 2017 because the death certificate took a few weeks to be processed ($100 000). The 3rd claim is only reported to the insurer in May 2017 because the family were not aware of the existence of the insurance policy with a sum assured of $1m. 

If no IBNR was considered at 31 December 2016, the claims experience would be understated and the financial statements would overstate profits by $1.1m (all else being equal). Or if the claims history were to be used for pricing without an ibnr, the claims would be understated which could lead to potentially incorrect premiums being calculated. 

Technical Aspect

It is used in general insurance for claim reserve calculation. Reserve calculation is necessary for the long-tailed claims (eg: motor claims) which takes many years to get settled.
One axis of the run-off triangle matrix (vertical one) denotes accident year and the other axis (horizontal one) denotes development year (or, delay year).
Accident year specifies in which year the claim is reported. Development year specifies after how many years of the claim reported it is getting settled.
The upper-left-side triangle is usually formed with paid claim amounts (sometimes with incurred claim amounts). The lower-right-side triangle is projection of future claim payments.
This projection is done either by using development factors or by using grossing-up factors.

In CT6 (statistical methods), we read about 4 methods of calculating reserves :
  1. Chain-ladder method,
  2. Inflation adjusted chain-ladder method,
  3. Average cost per claim method,
  4. Bornhuetter-Ferguson method. 
Source: Quora

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