Would you please explain why the offset is ln(exposure) in the claim numbers model? (MV models in pricing, chapter 17)
For the purpose of the ST8 exam you only need to know that for a claim numbers model you need an offset of Ln(exposure). You do not need to know the reason for this. If you wish to know more then it is probably worth searching the internet for papers on this subject, such as the Practitioners Guide to Generalized Linear Models by Anderson et al which parts of the core reading were based on.
Thank you Mr. Michaels! I did manage to download the paper you suggested..will go through it this weekend!
Simply speaking, we would model the claims number y for a portfolio composed of N risks. So the total claims number for the portfolio is equal to the number of risks(N) multiplied by the claims frequency of each risk. That is, y=N*exp(sum of bi*xi), or ln(y)=ln(N)+sum of bi*xi Here ln(N) is called the Offset. Hope it helps.
Accurately speaking, we are modelling the claims frequency per exposure. One way is to use the offset item. And another equavalent way is to work out the claims frequency per exposure in the database and fit the variable of claims frequency per exposure directly, using the exposures as the weights.
