Takaful - Role of an Actuary in Pricing

Pricing is an important part of Takaful because participants normally pay their contributions in advance, at the beginning of the coverage period, before anyone knows exactly what claims will occur during that period.

This creates an important problem:

The contribution must be determined today, even though the actual claims will only be known in the future.

Therefore, the actuary uses available information and assumptions about future claims to determine an appropriate contribution.

Two broad approaches to determining the risk contribution are:

Collective pricing

and

Risk-weighted pricing.

1. Why Is Pricing Necessary in Takaful?

Suppose Ahmad purchases medical Takaful on:

1 January

He pays his contribution at the beginning of the year.

However, the Takaful operator does not know whether Ahmad will:

make no claim

make one small claim

or

make several large claims

during the year.

Therefore:

Contribution is collected first

↓

Claims occur later

This means the contribution has to be determined based on an estimate of future risk.

2. The Actuary Cannot Know Future Claims Exactly

The actuary cannot predict exactly:

who will become sick

who will make a claim

how many claims will occur

or

how much each claim will cost.

Instead, the actuary uses:

historical claims data

statistical information

claim frequency

claim severity

participant characteristics

and other relevant risk information

to estimate the expected cost of claims.

Therefore:

Actuarial pricing is based on expected future claims, not known future claims.

3. What Does the Actuary Try to Achieve?

The actuary tries to determine an appropriate amount of tabarru’ so that the PRF has sufficient resources to support the risks accepted into the pool.

In simple terms:

Expected Risk → Appropriate Tabarru’ → PRF → Future Claims

If tabarru’ is too low relative to the risk:

Insufficient Tabarru’

↓

Claims may exceed PRF resources

↓

Greater risk of PRF deficit

Therefore, appropriate pricing is important for the financial sustainability of the Takaful arrangement.

4. What Is Collective Pricing?

Under collective pricing, participants in the relevant group pay the same or common tabarru’ amount, even though their individual risk levels may be different.

In simple terms:

Different risks → Same tabarru’

The contribution is based on the collective or average characteristics of the group rather than being individually adjusted for each participant’s specific risk.

5. Medical Takaful Illustration

Suppose four people want medical Takaful protection.

Risk 1

A 30-year-old in good health

Risk 2

A 50-year-old with high blood pressure

Risk 3

A 60-year-old with diabetes

Risk 4

A 20-year-old in very good health

These four people do not necessarily have the same probability of making a medical claim.

Within this simplified illustration, Risk 3 is assumed to have the highest expected claims risk, while Risk 4 has a much lower expected claims risk.

6. Different Participants Bring Different Risks

The important idea is:

Risk 1

Relatively lower expected risk.

Risk 2

Higher expected risk because of the assumed health characteristics.

Risk 3

Highest expected risk in this illustration.

Risk 4

Lowest expected risk in this illustration.

Therefore:

The participants do not bring equal expected claims risk into the PRF.

However, collective pricing does not necessarily distinguish between these different individual risk levels.

7. Same Tabarru’ Under Collective Pricing

Suppose the common tabarru’ is:

RM100 per participant

Therefore:

Risk 1 pays = RM100

Risk 2 pays = RM100

Risk 3 pays = RM100

Risk 4 pays = RM100

Total tabarru’ collected:

RM100 × 4 = RM400

Therefore, the PRF receives:

RM400

8. But Their Risks Are Not the Same

Although everybody contributes:

RM100

their expected claims risks differ.

For instance, within this simplified illustration:

Risk 4 may have a relatively low probability of making a claim.

Risk 3 may have a considerably higher probability of making a claim.

Yet:

Risk 4 pays RM100

and

Risk 3 also pays RM100.

Therefore, the tabarru’ does not directly reflect the individual risk each participant brings into the pool.

9. Why Might RM400 Be Insufficient?

Suppose the RM100 common tabarru’ was determined based on an assumed mixture of:

lower-risk participants

medium-risk participants

and

higher-risk participants.

If the actual group develops exactly as expected, the pricing may be more likely to work as intended.

But suppose the actual participants who join are mostly:

higher-risk participants

.

Then:

Total expected claims may be much higher

while:

Each person still pays only RM100.

Therefore, the:

RM400 total tabarru’ may be insufficient to meet total claims.

10. Simple Numerical Illustration

Suppose the actuarial expected claims costs are:

Risk 1 = RM60

Risk 2 = RM120

Risk 3 = RM180

Risk 4 = RM40

Total expected claims:

RM60 + RM120 + RM180 + RM40 = RM400

If all four participate and each pays RM100:

Total tabarru’:

RM400

Expected claims:

RM400

So the collective price appears to work.

But this depends on the expected mixture of risks actually remaining in the pool.

11. What If the Healthy Participants Do Not Join?

Suppose Risk 4 is very healthy and believes:

“RM100 is too expensive for the amount of risk I bring.”

Risk 4 decides not to participate.

Risk 3, however, has much higher expected medical costs and may think:

“RM100 is attractive for the protection I receive.”

Risk 3 therefore remains in the pool.

This creates a serious problem because the actual pool begins to contain a larger proportion of:

Higher-risk participants

than the actuary originally assumed.

12. This Is Called Anti-Selection

This situation is called:

Anti-selection

or:

Adverse selection

It occurs when participants have information about their own risk and the pricing structure makes the Takaful arrangement relatively more attractive to higher-risk participants than to lower-risk participants.

In simple terms:

The people who expect to claim more are more attracted to the common price, while people who expect to claim less may find the same price unattractive.

13. Why Would a Healthy Participant Leave?

Suppose:

Healthy participant

Expected claim cost = RM40

Tabarru’ = RM100

The participant may feel RM100 is expensive relative to their expected risk.

But consider:

Higher-risk participant

Expected claim cost = RM180

Tabarru’ = RM100

The RM100 contribution appears relatively attractive.

Therefore:

Lower-risk participant

Expected cost RM40 → Pays RM100 → May not join

while:

Higher-risk participant

Expected cost RM180 → Pays RM100 → More likely to join

This is how common pricing can affect the composition of the risk pool.

14. Why Is Anti-Selection Dangerous?

The original RM100 contribution may have been calculated assuming a balanced mixture of:

low risk + medium risk + high risk

But if many lower-risk participants do not join, the pool changes.

The new pool may contain:

More high-risk participants

Therefore:

Average expected claims increase

but:

Tabarru’ remains RM100

This creates a mismatch.

15. The Anti-Selection Process

The process can be understood as:

Same Tabarru’ for Different Risks

↓

Low-Risk Participants Find Price Relatively Expensive

↓

Some Low-Risk Participants Do Not Join

↓

High-Risk Participants Find Price Relatively Attractive

↓

Higher-Risk Participants Become a Larger Proportion of the Pool

↓

Average Expected Claims Increase

↓

Original Tabarru’ Becomes Inadequate

↓

Greater Risk of PRF Deficit

16. Why Is the Actuary’s Original Assumption Important?

Actuarial pricing depends on assumptions.

Suppose the actuary expects:

40% low-risk participants

40% medium-risk participants

20% high-risk participants

The RM100 tabarru’ may have been determined based on this expected mixture.

But suppose the actual pool becomes:

10% low-risk

30% medium-risk

60% high-risk

The actual risk profile is now much worse than assumed.

Therefore:

A collective price calculated using one expected risk mixture may become inadequate if the actual participants have a significantly different risk profile.

17. Collective Pricing Depends on the Composition of the Pool

This is the key weakness of collective pricing.

The common contribution may be adequate only if the actual composition of participants is reasonably consistent with the assumptions used when determining the price.

If the actual pool becomes much riskier:

Expected Claims ↑

while:

Tabarru’ per Participant stays the same

Therefore:

Probability of insufficient PRF funding ↑

18. Why Does Voluntary Participation Matter?

If participation is compulsory, lower-risk participants cannot simply leave because they consider the common contribution too high.

Therefore, the expected mixture of:

low-risk

medium-risk

and

high-risk

participants may be easier to maintain.

But if participation is voluntary:

Participants can decide whether the common contribution represents good value for their own circumstances.

This creates greater potential for anti-selection.

19. Collective Pricing Can Create Cross-Subsidisation

When everyone pays the same tabarru’ despite having different expected risk:

Lower-risk participants may contribute more relative to their expected claims

while:

Higher-risk participants may contribute less relative to their expected claims.

This creates:

Cross-subsidisation

For example:

Low-risk expected cost = RM40

Contribution = RM100

Higher-risk expected cost = RM180

Contribution = RM100

The lower-risk participant is effectively contributing relatively more toward the collective risk cost.

20. Is Cross-Subsidisation the Same as Risk Sharing?

No.

This distinction is important.

Risk Sharing

Means participants contribute to a common PRF and the fund collectively pays valid covered losses.

Cross-Subsidisation

Means one category of participants is systematically paying relatively more compared with its expected risk while another category pays relatively less.

Therefore:

Risk sharing is the fundamental pooling mechanism, while cross-subsidisation concerns how the cost of that pool is allocated among participants.

21. The Alternative - Risk-Weighted Pricing

One way to address the problem is:

Risk-Weighted Pricing

Under this approach, the amount of tabarru’ depends more directly on the risk that each participant brings into the pool.

Therefore:

Lower expected risk → Lower tabarru’

Higher expected risk → Higher tabarru’

The objective is to make contributions better reflect expected claims costs.

22. Simple Risk-Weighted Illustration

Suppose actuarial assessment produces:

Risk 1 expected risk cost = RM60

Risk 2 = RM120

Risk 3 = RM180

Risk 4 = RM40

Instead of charging everyone RM100, a simplified risk-weighted structure could charge amounts more closely related to those risks.

Therefore:

Risk 1 → Lower tabarru’

Risk 2 → Higher tabarru’

Risk 3 → Highest tabarru’

Risk 4 → Lowest tabarru’

The total contributions can then respond more directly to the actual risk composition of the pool.

23. Why Can Risk-Weighted Pricing Reduce Anti-Selection?

Suppose a lower-risk participant has an expected risk cost of:

RM40

Instead of charging RM100, the contribution is priced closer to the participant’s actual expected risk.

The participant is therefore less likely to feel that they are paying excessively relative to their risk.

At the same time, a higher-risk participant with an expected cost of:

RM180

would pay a higher tabarru’.

Therefore, the higher-risk participant is less likely to be severely underpriced.

So:

Risk-Based Contribution

↓

Less Underpricing of High Risks

• ●

Less Overpricing of Low Risks

↓

Reduced Anti-Selection Pressure

24. Contributions Are Paid Before Claims Are Known

The most important timing issue is:

At the beginning of coverage

The participant pays the contribution.

But:

During the coverage period

Claims emerge.

Therefore:

Time 0

Contribution determined and collected.

↓

Future period

Claims occur.

↓

Actual claims become known

The actuary must therefore estimate future claims before they happen.

25. Why Can’t the Operator Wait Until Claims Occur?

Suppose the operator said:

“We will wait until the end of the year, see who claimed, and then decide how much everyone should contribute.”

That would undermine the normal advance-funding structure of the Takaful arrangement.

The PRF needs resources available to pay claims when they arise.

Therefore:

Contributions must be collected before the actual claims experience is fully known.

This is why actuarial pricing is necessary.

26. Expected Claims vs Actual Claims

The actuary determines contributions based on:

Expected claims

But the PRF eventually experiences:

Actual claims

These will not necessarily be identical.

For example:

Expected claims = RM1 million

Actual claims could be:

RM800,000

RM1 million

or

RM1.3 million

Therefore:

Pricing is based on expectations, while the eventual financial result depends on actual experience.

27. Why Is There Uncertainty?

Future claims are affected by:

how many participants make claims

how severe the claims are

unexpected illnesses or accidents

medical-cost inflation

changes in participant behaviour

and other uncertain events.

Therefore, even a well-calculated contribution cannot guarantee:

Total Tabarru’ = Total Actual Claims

The objective is to set contributions on a financially sound basis given the information available.

28. What Happens If Tabarru’ Is Too Low?

Suppose:

Total tabarru’ collected = RM1 million

Actual claims and relevant obligations = RM1.3 million

Simplified shortfall:

RM1.3m − RM1m = RM300,000

This creates financial pressure on the PRF and may contribute to:

PRF deficit

Therefore, underpricing can threaten the financial sustainability of the risk pool.

29. What Happens If Claims Are Lower Than Expected?

Suppose:

Total relevant PRF income = RM1 million

Relevant claims, expenses and provisions = RM800,000

Simplified positive result:

RM1m − RM800,000 = RM200,000

This may contribute to an:

Underwriting surplus

However, the existence of surplus does not automatically mean the entire RM200,000 should immediately be distributed.

The PRF’s future obligations and financial strength still need to be considered.

30. The Actuary’s Main Pricing Responsibility

The actuary needs to consider questions such as:

What risks are entering the pool?

How frequently are claims expected?

How severe are those claims expected to be?

What participant characteristics affect the risk?

What total claims are expected?

What tabarru’ should be collected?

and

Could the pricing structure create anti-selection?

Therefore, actuarial pricing is not simply:

“Choose a contribution amount.”

It is about ensuring that the contribution structure appropriately reflects the expected risk of the pool.

Easy Way to Remember

PRICE TODAY → CLAIMS TOMORROW

The contribution is determined:

Before claims occur

Therefore, the actuary must:

Estimate Risk

↓

Estimate Future Claims

↓

Determine Appropriate Tabarru’

↓

Collect Contributions

↓

PRF Pays Future Covered Claims

Collective Pricing - Easy Formula

Different Risks → Same/Common Tabarru’

For example:

Risk 1 → RM100

Risk 2 → RM100

Risk 3 → RM100

Risk 4 → RM100

Total:

RM400

The problem arises if the actual risk composition is worse than the assumptions used to determine RM100.

Anti-Selection - Easy Formula

Same Price + Voluntary Participation

↓

Low-Risk Participants May Find Price Too High

↓

High-Risk Participants May Find Price Attractive

↓

Pool Becomes Higher Risk

↓

Expected Claims Increase

↓

Original Contribution May Become Inadequate

Risk-Weighted Pricing - Easy Formula

Different Risks → Different Tabarru’

Therefore:

Lower Expected Risk → Lower Tabarru’

and:

Higher Expected Risk → Higher Tabarru’

The objective is:

Tabarru’ More Closely Reflects Expected Risk

Most Important Concept

The main problem is not simply that participants have different risks.

The real problem occurs when:

A common contribution is calculated using an assumed mixture of low-risk and high-risk participants, but voluntary participation causes the actual pool to contain disproportionately more high-risk participants.

Then:

Actual Pool Risk > Expected Pool Risk

while:

Tabarru’ remains based on the original assumptions

which can lead to:

Insufficient PRF Funding

One-Sentence Summary

The actuary determines Takaful pricing before actual claims are known by estimating the expected risk of participants; under collective pricing, participants with different risk levels pay a common tabarru’ amount, which can encourage anti-selection when lower-risk participants find the price unattractive while higher-risk participants are attracted to it, potentially making the actual risk pool more expensive than assumed and causing the tabarru’ collected to become insufficient for future claims.