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abcd. Stochastic Reserving in General Insurance Peter England, PhD EMB. Younger Members’ Convention 03 December 2002. Aims. To provide an overview of stochastic reserving models, using England and Verrall (2002, BAJ) as a basis.
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Younger Members’ Convention
03 December 2002
Assume that the data consist of a triangle of incremental claims:
The cumulative claims are defined by:
and the development factors of the chain-ladder technique are denoted by
(Chain ladder type)
Other constraints are possible, but this is usually the easiest.
This model gives exactly the same reserve estimates as the chain ladder technique.
In general, remembering that
Prediction variance=process variance + estimation variance
Prediction variance = process variance +
Estimation variance is larger for ODP than NB
Process variance is larger for NB than ODP
End result is the same
To estimate ultimate claims using the chain ladder technique, you would multiply the latest cumulative claims in each row by f, a product of development factors.
Hence, an estimate of what the latest cumulative claims should be is obtained by dividing the estimate of ultimate by f. Subtracting this from the estimate of ultimate gives an estimate of outstanding claims:
Let the initial estimate of ultimate claims for accident year i be
The estimate of outstanding claims for accident year i is
replaces the latest cumulative claims for accident year i, to which the usual chain-ladder parameters are applied to obtain the estimate of outstanding claims. For the chain-ladder technique, the estimate of outstanding claims is
Put a prior distribution on the row parameters.
The Bornhuetter-Ferguson method assumes there is prior knowledge about these parameters, and therefore uses a Bayesian approach. The prior information could be summarised as the following prior distributions for the row parameters:
“I believe that stochastic modelling is fundamental to our profession. How else can we seriously advise our clients and our wider public on the consequences of managing uncertainty in the different areas in which we work?”
- Chris Daykin, Government Actuary, 1995
“Stochastic models are fundamental to regulatory reform”
- Paul Sharma, FSA, 2002
England, PD and Verrall, RJ (2002) Stochastic Claims Reserving in General Insurance, British Actuarial JournalVolume 8 Part II (to appear).
Verrall, RJ (2000) An investigation into stochastic claims reserving models and the chain ladder technique, Insurance: Mathematics and Economics, 26, 91-99.
Also see list of references in the first paper.
G e n e r a l I n s u r a n c e A c t u a r i e s & C o n s u l t a n t s