Actuarial Expectation Comparison

#1
Hey there. I work as an actuary. Interestingly a lot of the industry has very little understanding of statistics. The most commonly used models are GLM (primarily for yearly contracts), this is primarily used to determine what factors are significant with regards to claims/lapses etc.

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
 
#2
I should add. I had considered some sort of binomial family for the GLM. The problem is two fold, firstly that estimates the actual parameters not how far off current assumptions we are, and secondly it's binomial in a sense but the outcome is not 0 or 1, it's 0 or the sum insured. So that doesn't really work....
 

hlsmith

Less is more. Stay pure. Stay poor.
#3
Yeah, if I followed you should be able to model this with a GLM, you may just need to get your dispersion right. I believe one compares actual plotted data to the fitted model to examine for overdispersion, with the negative-binomial being one alternative to a poorly fitted Poisson.

Can you be a little more explicit in what you are looking for with variance or what the outcome of interest is given your data?