The smartphone has brought a lot of useful functionality to our lives. There’s an app for nearly everything from ordering flowers to finding your way in strange lands. Yet, while there have been many improvements in the area of health; such as the heart monitoring functions and pedometers – you’ve still always had to visit a GP when something goes wrong.

The Problem

Recent material published in The Guardian shows that GP services simply aren’t keeping pace with the way we live our lives. Fewer than 1 in 3 people is offered a same day appointment. Many surgeries are offering endless queue systems where you have to turn up to the surgery and wait, and wait, until you’re called.

Doctors don’t seem to like the way we work either – surgeries are still mainly on weekdays and during the day time. We understand that like most of us, they have families too but it means a visit to your GP is always going to come out of the working day. Our employers aren’t always as understanding about this as they might be or in the case of small businesses – they simply can’t afford to lose people for a day at a time for minor medical issues.

This leads to people seeking treatment at Accident and Emergency; for things which are neither accidents nor emergencies. The health service is feeling the pressure and while the NHS may still be free – it’s not delivering on the premise of basic care conveniently.

The Solution?

Enter Babylon Health. In partnership with BUPA, Aviva and AXA they’re changing the way that we can access treatment and integrate medical care into our busy and inflexible lives. The means of this change? An app for your smartphone; well an app for your Apple or Google Android phone at the moment; Windows phone users, all 4 of them, will have to wait for the moment.

This app offers a range of monitoring services using a series of in depth monitoring systems; nothing particularly new there – though they do bring together services that otherwise might require multiple apps.

It then goes on to offer face-to-face doctor’s appointments over the smartphone. This does cost money – you either need to pay by monthly subscription (5 quid a month brings you unlimited access to the service), on a one-off basis (£29 per appointment), or have this included in your health insurance policy.

You can also order prescriptions via the app and have them delivered. Then there’s the handy benefit of being able to access your own medical records whenever you want to – though you might want to be careful about this; hypochondria can result from spending too much time worrying about health issues.

For the insurers involved – the benefit almost certainly comes in the form of data generated by the monitoring suite. For the busy working person – the benefits are completely clear.

Babylon Health App and Insurance

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Last month, we took a look at the way an insurer would have to operate if they only insured a single party. As we discovered, it would be a hard business to run and not a very profitable one if an insurer only dealt with a single incidence of risk. They’d need to keep reserves equivalent to the maximum possible pay out under the policy and the premiums would be unlikely to support this kind of ring fencing of cash.

Fortunately, that’s not how insurance works – insurance is all about combining similar risks from many parties in order to share some of that risk and for insurers to be able to charge reasonable premiums and still make a profit.

The Loss Formula for Multiple Parties

Our simple loss formula needs an update at this point; it’s going to look something like this:

(Where X is the loss and N is the number of losses in the year.)

First Formula - Insurance Risk Modelling

The trouble with this formula is that it is clear that the loss is going to vary from year to year; some years will be better for our insurer in that they will beat the odds and their insured parties will have fewer accidents than the average and some years will be worse when they also beat the odds but their insured parties have more accidents than the average.

There are two things we need to know for this; the first is the distribution of loss and the second is the frequency of loss for the risk.

This is where the maths gets a bit more complicated.

The Distribution of Loss

This will normally be calculated using a Pareto distribution. Where the α depends on the specific risk. For our car insurer they’d have to calculate this distribution based on the chances of theft, fire, mechanical failure, etc. and then combine the results.

Pareto Distribution

 

The Frequency of Loss

The frequency of loss can be calculated in many ways but one of the simplest ways to do so is with a Poisson distribution. This only works well in the event that losses are unrelated and relatively rare so it might not be suitable for all types of premium calculation.

Poisson Distribution

 

These two formulae can then be used to work out the total expected losses in multiple years; to some degree of certainty. You can then treat the expected loss in any given year as an average of the possible losses across multiple years.

However, there’s still more complexity to add to this model and that’s what we’ll be looking at in the next part of this series next month.

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