Context: actuarial science, insurance, outstanding claims
(= Incurred but not reported) A term used in insurance (particularly general insurance) and actuarial science. The value of losses that have already incurred, but not yet claimed.
To quote an example from Deegan (Australian Financial Accounting, 2nd ed., 1999):
For example, there may have been a bushfire towards year end in an area in which a number of policy holders reside. Even if no claims have been made, an estimate of probably claims should be possible.
Perhaps an example would help. Suppose you have car insurance, and you have crashed your car on 29 June, but did not tell the insurance company until 1 July. Usually an insurance company closes its books on 30 June. Thus your claim has been incurred on one financial year but not reported until the next. The value of your claim would be part of IBNR estimates.
Calculating the IBNR for any particular period is done by an actuary. To do so, he/she will need to take into account the previous claims experience of the insurance company, the past and future inflation rates, claims inflation (how inflation-adjusted claim sizes still increases each year because the company has written more policies) and the loss ratio.