Actuarial pricing, capital modelling and reserving

Pricing Squad


Issue 11 -- February 2017

Welcome back to Pricing Squad!

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

Today's issue shows how GLMs can damage your portfolio when used in conjunction with other pricing models.

You can also read a review of Pietro Parodi's pricing textbook.


Granularity conflicts

Mr Reilly's spies

Mr Reilly employs three spies. Every month he pays agent X 180, agent Y 100 and agent Z 50.

The agents send Reilly intelligence reports. The reports are anonymised so Reilly does not know which of the three agents authored any given report.

One day, Reilly's agency orders him to cut his spy budget because the value added per spy was 100 only. This is 10% below the current average cost of 110 per spy.

Reilly thinks: 'Historical reasons behind the pay scale are clearly obsolete. At 100 per spy, agent X sure looks overpaid by a big margin! Cutting X's salary alone would solve my problem. But wait, maybe X provides the best intel. What if he defects? Better cut Y or Z instead. What should I do?'

Reilly faces a "granularity conflict". He must make a decision using two pieces of information which are incompatible. On the one hand he has a granular payroll. On the other hand he has an unsegmented new budget.

Granularity conflicts in ratemaking

Car Insurance Ltd built a very predictive loss cost GLM.

After generating each renewal invite, they score the invite with this GLM. Next, they divide the predicted loss cost by the quoted premium to derive "scored loss ratio". Finally, they adjust the invited premiums accordingly.

Everybody cheers this clever hack.

But despite the increased pricing sophistication the actual renewal loss ratio deteriorates. This is blamed on increased bodily injury claims, the underwriting cycle and changes to the business mix.

The true cause remains undetected for years.

Granularity conflicts under the surface

A good personal lines motor pricing algorithm is organic.

There are hundreds of pricing rules, exceptions and interactions introduced by generations of analysts and underwriters.

No single person understands all of the rationales behind all pricing calculations. This is OK. It might seem messy, it might be annoying, but it's OK.

Unbeknown to them, when Car Insurance Ltd compares their organic pricing algorithm with a GLM prediction, they face a granularity conflict. By necessity, the GLM simplifies complex interactions, exceptions and classifications. Therefore, it is less granular than the rating algorithm.

Let's say that the existing pricing algorithm differentiates between a "drink driving" conviction 3 years ago and the same conviction 4 years ago. Two otherwise identical drivers with past drink-driving convictions will be quoted differently if they were convicted in different years.

But a GLM is unable to reflect such tiny levels of granularity for a single conviction type.

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