GLMs - prior weights, single risk premium model

[Howard O'Connor]

Hi all
1) The GLMs chapter mentions prior weights (e.g. 1 for claim numbers, exposure for claim frequency).
What is the meaning of prior weights and how are they used in modelling?
2) What is a 'single risk premium model'?
Many thanks

 

[Katherine Young]

1) Imagine you have a 10 policyholders aged over 90 but 10000 policyholders aged between 20 and 30. You want your model output to be influenced more by the 10000 policies than by the 10 policies. The weights allow you to do this.
2) You would combine your frequency and severity models to get an estimated risk premium. (In other words, frequency * severity = burning cost.)

 

[Howard O'Connor]

Re your answer to question 1, what are you measuring in your scenario? How would you use weights to do this?
Many thanks

 

[Katherine Young]

The prior weights allow information about the known credibility of each observation to be incorporated in the model. For example, if modeling claims frequency, one observation might relate to one month's exposure, and another to one year's exposure. There is more information and less variability in the observation relating to the longer exposure period, and this can be incorporated in the model by defining ωi to be the exposure of each observation. In this way observations with higher exposure are deemed to have lower variance, and the model will consequently be more influenced by these observations.

This is quite technical Howard. For more information, see the original source of the Core Reading, https://www.casact.org/pubs/dpp/dpp04/04dpp1.pdf