Actuarial pricing, capital modelling and reserving

Pricing Squad

Issue 18 -- September 2017

Welcome back to Pricing Squad!

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

Today's issue is about minimum premiums.

I am also offering a one day Access Hacks for Actuaries course for those of us who use MS Access in pricing.

Minimum premiums

Whoever can be trusted with very little can also be trusted with much (and vice versa).
- Jesus from Nazareth

It is easy to forget about minimum premiums when modelling. The two examples below show why you should not.

Example 1 - minimum premiums in burning cost models

Two burning cost models were fitted to the same data set.

The first model is purely multiplicative, a standard GLM.

The second model has one extra parameter only. Minimum premium is estimated together with the multiplicative parameters. The second model is therefore non-linear. (For one way to build such models, see Pricing Squad from January 2017.)

Since the second model accounts for the minimum premium, it can offer bigger discounts than the first model. That is because full discounts apply to some policies while they are mitigated by the minimum premium for other policies.

The table below shows estimated "no claim discounts" with and without minimum premium included in the model.

For nine years claim free driving the difference between the two models is 6%. This could easily translate to a £50-£200 or greater difference in quoted premium for some drivers.

Example 2 - min premiums in elasticity modelling

In your products, do minimum premiums apply before or after the randomised price test perturb?

Sometimes it applies after. And people often forget to account for this.

This results in serious understatement of elasticity, especially in low risk segments. The end result is overpricing and draining of low risk segments.

The chart below shows elasticity of a motor book (modelled, smoothed, internet, new business) by age band calculated with and without accounting for the minimum premium.

A very significant difference indeed.

So do not forget about your minimum premiums!

Access Hacks for Actuaries

"I hate Access... would love to never see it again" -- responded a friend when I raised the subject. If your share her frustration and yet you need to work with MS Access anyway, I now offer a one-day Access Hacks for Actuaries course which will help.

The course covers:

  1. What works well with MS Access, what are the limitations and how to hack them.
  2. VBA for Access. Introduction to coding and automation.
  3. SQL for Access. Keeping clean and formatted SQL queries. Advanced SQL: keys, switch, group by, having and more.
  4. Good data hygiene for actuaries. Safe import-export, integrity via keys, easy deduplicating, reconciliations.
  5. ProInsurance (Access) module: import, integrity, process claims, process premiums and more.

The course allows plenty of time for questions, discussion and learning through practice tasks. It can be delivered in person or via Webex. The price is £485 per person + VAT with discounts for groups and for Pricing Squad readers.

Email me on or call +44 787 519 5807 if you want to book Access Hacks for Actuaries today.

Copyright © 2017 Jan Iwanik, All rights reserved. You are receiving this email because you subscribed to updates from We publish data and analysis for informational and educational purposes only. You can unsubscribe from this list by emailing us.