Actuarial concepts for successful negotiations with insurers

John Maynard Keynes said, ‘In the long run, we're all dead.’

Fortunately, in insurance, the reality is more cheerful: ‘In the long run, we all agree.’

In insurance, all interests are aligned over the long term. This is not a matter of good thinking, but of reality. It is only in the long term that the eternal trio - broker, insurer and reinsurer - can find a common ground. The broker through customer loyalty, the insurer through the profitability of its programme and the reinsurer through the stability of its positions.

But our daily lives are also governed by the short term: an obligation to achieve results, faltering profitability, and so on.

Discussions often get heated.

To keep a cool head in these heated moments, we turned to Nabil Seddiki. An actuary and pricing expert at Seyna, he is responsible for co-designing insurance products with brokers in various insurance verticals.

The aim of this article is to provide 3 actuarial concepts and their concrete applications to generate new angles of discussion with your insurance partners.

These are the keys to speaking the same language, and building stable, profitable programmes for everyone, over the long term.

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Poisson's law

Concept and application

Named after its author, the French mathematician Siméon Denis Poisson, Poisson's law is a statistical law that allows you to count a number of events in a given time interval.

For example, if you want to estimate the number of red cars passing in the street under your window, you can use Poisson's law.

In insurance, this is a very common tool. This law is used to estimate the frequency of random, independent events occurring at a constant average rate. This makes it possible to incorporate uncertainty into the modelling and anticipate possible outcomes. It is widely used for risks such as mechanical breakdowns, ticket cancellation insurance or the breakage of electronic equipment.

This law admits only one parameter: frequency, and everything is based on it. So, in our pricing, this parameter is fundamental.

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Some ideas for your next meeting:

Bear in mind the concept of Poisson's law. In other words, what levers can you pull to limit the frequency of claims? Here are a few ideas ...

• Reinforce prevention around your device by combining the sale of insurance with smartphone protection from the distributor
  
  This is a classic prevention scheme, but some interesting variations have been developed in recent years. In fact, some programmes have started to offer no-excess or accelerated compensation to anyone who has adopted the preventive measures recommended by the insurer. These schemes are sometimes used as part of cycle insurance programmes, for example, subject to the use of a certain brand of connected lock. The impact on Loss Ratio ends up being significant.
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• Include in the contract an annual overhaul of a household's electrical appliances by a reconditioning partner
  
  The aim is to prevent a small loss from turning into a disaster. Generating leads for a third-party service could provide additional income for your programme.
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• Generating educational content for social networks
  
  As well as improving prevention around your programme, this approach will generate more frequent contact with your community and help your brand to grow. You can even find insurance prevention on Tik Tok, why not you?

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Credibility Theory

Concept and application

Credibility theory is used to determine the extent to which historical data for a specific group (such as a group of policyholders or a market segment) should be taken into account in relation to overall industry data. It allows premiums to be adjusted according to the specific characteristics of a group, which can be crucial for particular market segments.

Without betraying any professional secrets, an actuary likes to explore risk. Cutting it from every angle. Credibility Theory is what allows us to consider a sample of risks as ‘outside the norm’, and therefore to give it its own specific analysis.

Individual or affinity health insurance is a good place to play, for example. But building an innovative offer for your customer will depend on our joint ability to prove that it responds to a different risk parameterisation than the national average.

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Some ideas for your next meeting:

• Recover as much claims history as possible
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  Our Anglo-Saxon friends say ‘Show, don't tell’. In other words, don't say it's a great programme, prove it. Arrive with as much data as possible. This is what will enable your insurance partner to get started.
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• Proving reduced exposure to risk
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  Insuring risk properly starts with knowing how policyholders behave. Do you offer ticket cancellation policies for events (concerts, shows, etc.)? For example, if the events you want to insure are in high demand and very popular (Hellfest, a Beyoncé concert or the Champion's League final), the insured population will be much less likely to cancel. It's not just a question of ticket volumes, but above all of data and knowledge of your customers. In fact, small local events can also have a lower claims rate because of the loyalty of the population. The key is to be able to justify it.‍

• Diversify the activities covered by your policy
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  Make sure that there are no related activities to be covered that are not very likely to cause claims, which would enable you to broaden the premium base without damaging the technical performance of the programme. An interesting case study: as a complement to your individual health policies, you can offer personal accident cover, which offers better margins than health and allows risk diversification.

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Remember, we all have an interest in insuring new programmes, whether we are brokers, insurers or reinsurers. Without business, no pooling is possible. However, our collective challenge is to get off to a good start so that we can guarantee profitable and therefore sustainable programmes.

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Game Theory

Concept and application

Game theory is used to model the strategic interactions between insurers and policyholders, particularly with regard to anti-selection and moral hazard. Although these two concepts represent the ABCs of actuarial science, they are often undervalued or poorly understood. They continue to lead to the downfall of contracts right from the outset, particularly in the case of health risks.

Our mission as insurance professionals is to build programmes that protect as many people as possible, for as long as possible. To achieve this, we need to minimise opportunistic behaviour.

• Anti-selection: Policyholders with a higher risk are more likely to take out insurance, which can lead to an increase in claims. Using game theory, an actuary can design contracts that also attract low-risk individuals, for example by offering reduced premiums.
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• Moral hazard: policyholders may change their behaviour after taking out insurance, by taking more risks. Game theory can help to design contracts with incentives that encourage prudent behaviour.

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Some ideas for your next meeting:

• Setting up a franchise
  
  The concept is not revolutionary. It even seems outdated in a sector where we are striving to make our offers ever more transparent. What will make the difference in your discussions, however, is remaining open to these mechanisms. We all agree that a product without a franchise makes it clearer and avoids disappointment. Yet statistics show that deductibles significantly improve underwriting results by making policyholders face up to their responsibilities.

• Implementing a bonus-malus system
  
  These systems provide for an increase in premiums after a claim has been made, or a reduction in premiums if no claims have been made. They have the merit of providing an incentive and are generally better accepted by policyholders.

• Suggest a grouping approach to your insurer
  
  If you are covering another similar programme, offer to place this risk with your potential new partner to balance the overall risk.

• Dilute the risk of anti-selection by making offers to populations with fewer claims
  
  This means knowing the claims experience down to the smallest guarantee and being able to react quickly. And to do that, you need to have a good grasp of the data. Giving yourself the means to exploit it is not a cost but an investment that has a direct impact on your profitability. How can we do this? Refining provisions, identifying wavering segments... here are a few concrete examples of applications at Seyna.

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These few ideas are not intended to be exhaustive, but to provide new angles for discussion. In insurance, the magic happens when all the links in the chain work together towards the same result. When everyone focuses on what they do best. The broker focuses on customer knowledge and distribution, the insurer focuses on product development and the reinsurer focuses on risk and financial management.

Knowing, understanding and adopting the other person's language means giving yourself the means to win in the long term.

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