The question I am trying to answer is the following. So in actuarial, we have a tonne of assumptions (i.e. mortality rates by age and gender). The question we are usually trying to answer is "has our experience been significantly different from our current assumptions to justify a change in assumptions". I can usually do this by hand with for example a claim on a policy with sum insured S, E[X]=pS and E[X^2]=S^2p, i can then derive the variance for the whole portfolio.

I am wondering if there is a better way to do this with regression. The data looks as follows: Explanatory Variables|ExpectedClaims|ActualClaims.

With a line for each individual. Does anyone have any ideas as to how you might be able to do this with some form of regression instead of having to manually calculate the variance and expectation.

I have tried using a quassipoisson with ActualsCLaims~Offest(ExpectedClaims)+Explanatory, and this gives a good indication of potentially significant variables and the quantum of this, but it tends to underestiate the variance (for example one group where i calculated the variance manually is nowhere near significant, but the GLM is saying this grouping is very significant).

Any help would be appreciated.

Thanks,

Evan