Actuarial pricing, capital modelling and reserving

Pricing Squad


Issue 25 -- June 2018

Welcome to Pricing Squad

Pricing Squad is the newsletter for fellow pricing practitioners and actuaries in general insurance.

Today's issue warns you about reckless use of GLMs.


Modelled and non-modelled cuts in GLMs

I wish it was hard to "score" individual policies with a GLM.

Unfortunately, it is easy.

So, all policies get scored. Then decisions are made for individual policies based on the scores.

Bad decisions. Like lapsing business with high scored loss ratios. Or attracting policies with high scored life time values.

Break a GLM

GLMs do not predict well for individual policies. They were never meant to.

You can think of a GLM as a set of univariate models estimated across many variables simultaneously. These univariate models fit well for all variables at once when they are multiplied together. They nicely eliminate double counting of risk effects.

This is different, and less, than having a model predicting for each policy.

You do not have to take my word for it. Below is a chart showing a real GLM retention prediction by "scored loss ratio" and actual retention for a household book of business.

Yet, the same model fits well by other one-way cuts, for example by predicted retention bucket:

Why?

Because "scored loss ratio" is not an explicit factor in this model. (And should not be.)

Examples of common GLM-breaking segments are:

  • street price when it uses non-modelled factors, e.g. underwriting discounts
  • predicted claim divided by street price, a.k.a. "scored loss ratio"
  • predictions from another model which is sufficiently different, for example an elasticity model

Clear thinking

Think in terms of "modelled" cuts. A modelled cut is a segmentation included, or at least tested, in a predictive model.

Modelled cuts are the upper limit of legit GLM applications. For example, if owner's age was tested in a GLM then this GLM can support business actions based on age.

Do not let the ease of "scoring" datasets deceive you. Never make business decisions which rely on non-modelled cuts.


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