Insurance Premium Modelling – An Introduction

This week, we’re going to start looking at the basics of how premiums are calculated and over the next couple of months; we’re going to see how these models become more complex and how what initially, seems like an easy task, isn’t quite so simple.

The Basics of Insurance Premium Calculation

Let’s say that you were going to start you own insurance business tomorrow. You will begin by offering automotive insurance. One of your friends has approached you and wants to be your first customer and you’re trying to figure out how much you need to charge your friend and also how much you need to keep as a cash reserve in order to meet any claims your friend may make.

What Do You Need to Know?

Well, ideally you would need to know the following data:

  • How many times a year does your friend crash his car or have another incident that requires an insurer’s intervention? We could give this number a variable name such as “f”.
  • How much, on average, will it cost to repair his car in the event of a claim? “X”

The average loss per year on the contract, “s” then becomes:


Once you have that figure that’s the minimum you need to cover in premiums otherwise you’re going to make a loss.

However, most insurers don’t run to break even. They need to make a profit so you’re going to have to add a percentage on top of that figure in order to ensure your business can pay its operating costs and shareholders.

Now, this sounds simple enough but what about your reserves? How much money do you need to keep in reserve for this policy?

Calculating Your Reserves – The Basics

Now you face something of a conundrum. If you are only going to issue a single auto-insurance policy to your friend – you’re going to have to ensure that you have reserves available to pay out in the event of a claim.

In the case of a single policy that reserve amount “r” is going to have to be equal to the maximum possible loss “m” on that policy. That could be the entire value of the car, the contents and any other insured items (3rd party property, health care costs, etc.).

So to put that as a formula:


This is why insurance cannot work on an individual basis. Your premiums may work out to be £500 a year but if you have to keep £100,000 on hand to cover the pay out in the event of total maximum loss… it’s not going to be a very attractive way to do business is it?

So insurance works by combining risks; when you have hundreds or thousands of insured parties you can work out the likelihood of any and all of them having an accident within a given timeframe and base your premium calculations on the likelihood of those losses but your reserve is likely to be much smaller, proportionately to the number of insured parties, than it would be for a single party.

We’ll look at the basics of this in the next part of this series in a month’s time.


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