Economic Modelling · Role of insurance in reducing or removing risk

Limits of Insurance: Moral Hazard and Adverse Selection

Q: What is the difference between moral hazard and adverse selection?

Adverse selection is hidden information before the contract: higher-risk people are more likely to buy cover. Moral hazard is changed behaviour after the contract because the insurer bears part of the loss. Both come from asymmetric information.

Q: How do insurers control adverse selection?

They use underwriting, such as proposal forms and medical checks, and risk-based premiums. They may also use waiting periods, exclusions for existing conditions, and compulsory or group cover so that healthy people cannot easily opt out.

Q: What is the role of deductibles and excesses?

They make the policyholder pay the first part of each loss. This keeps an incentive to avoid loss and discourages small or inflated claims, which reduces moral hazard and lowers the premium.

Q: Does reinsurance solve moral hazard?

No. Reinsurance lets the insurer pass part of its claims risk to another company. It reduces the insurer's exposure and volatility, but it does not change how the original policyholders behave.

Updated 11 October 2026 · Fact-checked

Adverse selection occurs before the contract: high-risk people are more likely to buy cover, and the insurer cannot see who they are. Moral hazard occurs after: being insured changes behaviour and raises the chance or size of loss. Insurers respond with underwriting, risk-based premiums, excesses, deductibles, limits, co-insurance and reinsurance.

Understand Limits of Insurance: Moral Hazard and Adverse Selection

Insurance works by pooling many similar risks. This only works if the insurer can price the risk fairly. The problem is asymmetric information: the policyholder knows more about their own risk than the insurer does.

Adverse selection is a problem of hidden information before the contract starts. People who know they are high risk find insurance more attractive. If the insurer charges one average premium, low-risk people see it as poor value and leave. The pool then gets riskier, claims rise, the premium rises, and more good risks leave. This can end in a market that shrinks or fails, sometimes called an adverse selection spiral.

Moral hazard is a problem of changed behaviour after the contract starts. Once insured, the person bears less of the cost of a loss. So they may take less care (ex-ante moral hazard) or claim more or exaggerate a claim (ex-post moral hazard). An insurer cannot fully observe effort or care.

The insurer's tools target each problem. Against adverse selection: underwriting (proposal forms, medical checks, claims history), risk classification with different premiums for different groups, waiting periods, and compulsory or group cover so that healthy people cannot opt out. Against moral hazard: excesses and deductibles (the policyholder pays the first part of each loss), co-insurance (the policyholder pays a share), policy limits, no-claims discounts, and policy conditions with claim investigation.

The key link to utility theory: full cover at fair price removes all the policyholder's risk, so they have no financial reason to avoid loss. Partial cover keeps some of the cost with them, which restores the incentive to take care. Reinsurance does not cure either problem in the original policyholder. It lets the insurer pass on part of the resulting risk, and reinsurers often require the insurer to keep a share so that the insurer's own underwriting stays careful.

Key rules to remember

Claim paid with a deductible (fixed amount d): Payment = max(X − d, 0); X is the loss. The policyholder bears min(X, d). Excess and deductible are used for this in IAI material; state which meaning you use.
Claim paid with co-insurance share α: Payment = α × X, where 0 < α < 1; The policyholder bears (1 − α) × X of every loss.
Deductible with a policy limit L: Payment = min(max(X − d, 0), L); Use when cover has both a deductible and a maximum payout.
Fair premium (no expenses or profit): Premium = E[payment]; Loadings are added on top for expenses, profit and risk.
Adverse selection pricing with mixed groups: Average premium = Σ (proportion in group i × expected claim of group i); Valid only if the mix of groups stays fixed. If low risks leave, the proportions change and the premium must be recalculated.

How to solve Limits of Insurance: Moral Hazard and Adverse Selection questions

Use this for both written and multiple-choice questions on information problems in insurance.

1Identify the timing. Before the contract and hidden risk type points to adverse selection. After the contract and changed behaviour points to moral hazard.
2State the information asymmetry in one line: who knows what that the other party does not.
3Describe the effect on the insurer: claims higher than priced, a worse risk mix, or a rising premium.
4Name the matching control. Use underwriting, classification, waiting periods or compulsory cover for adverse selection. Use excesses, deductibles, co-insurance, limits or no-claims discounts for moral hazard.
5Explain why the control works, in terms of incentives or information revealed.
6If numbers are given, calculate the payment or expected claim using the formulas, and state assumptions such as a fixed mix of risks.
7Mention limits and side effects: controls cost money, may reduce cover for genuine claimants, and reinsurance only transfers risk.

Quickest way: Before or after the contract test

When to use it: Multiple-choice questions and short written parts that ask you to classify a situation or pick a remedy.

Ask: did the behaviour or knowledge exist before the policy was bought? If yes, adverse selection.
Ask: did the person change what they do because they are now covered? If yes, moral hazard.
Pick the remedy that matches: information tools for the first, shared-loss tools for the second.
For a numeric payment, apply max(X − d, 0) first, then any co-insurance or limit.

Common mistakes in Limits of Insurance: Moral Hazard and Adverse Selection

Mixing up moral hazard and adverse selection.
Both come from asymmetric information and both raise claims.
Fix: Use timing. Hidden type before purchase is adverse selection. Changed behaviour after purchase is moral hazard.
Saying deductibles solve adverse selection.
Deductibles reduce claims, so students assume they fix risk mix generally.
Fix: Deductibles mainly address moral hazard. They can also help sort risk types, since high risks prefer low deductibles, but state that as a secondary point.
Applying a deductible wrongly, for example paying X − d when X < d.
Forgetting the floor at zero.
Fix: Always write max(X − d, 0). If the loss is below d, the insurer pays nothing.
Saying reinsurance removes moral hazard or adverse selection.
Reinsurance is described as risk reduction for the insurer.
Fix: Say it transfers part of the resulting claims risk and can stabilise results. It does not change the policyholder's behaviour or risk type.
Claiming a single average premium is fair when risk groups differ.
Ignoring that the mix of buyers changes with the price.
Fix: Show that low risks may leave, so the true expected claim per policy rises above the average calculated at the old mix.
Giving only definitions in a written answer.
The question seems to ask for a simple explanation.
Fix: Add cause, effect on the insurer, one control and why it works. Answers that explain the mechanism earn more marks.

Worked examples

Example 1

A health insurer charges one premium to a group in which 50% are low risk (expected annual claim ₹10,000) and 50% are high risk (expected annual claim ₹30,000). (a) Find the fair premium if both groups buy. (b) Suppose all low risks leave. What is the new fair premium? Name the effect.

Show the solution

(a) Average expected claim = 0.5 × 10,000 + 0.5 × 30,000 = 5,000 + 15,000 = ₹20,000.
(b) If only high risks remain, the expected claim is ₹30,000, so the fair premium becomes ₹30,000.
The premium rises by ₹10,000 because the risk mix worsened.
This is adverse selection: the low risks found ₹20,000 poor value compared with their expected claim of ₹10,000.

Answer: (a) ₹20,000. (b) ₹30,000. The effect is adverse selection, caused by the insurer being unable to tell the groups apart.

Example 2

A motor policy has a deductible of ₹5,000. Losses are ₹3,000, ₹8,000 and ₹20,000 in three separate incidents. (a) Find the insurer's payment on each. (b) Explain how the deductible reduces moral hazard.

Show the solution

(a) Payment = max(X − 5,000, 0).
Loss ₹3,000: max(−2,000, 0) = ₹0.
Loss ₹8,000: 8,000 − 5,000 = ₹3,000.
Loss ₹20,000: 20,000 − 5,000 = ₹15,000.
Total insurer payment = 0 + 3,000 + 15,000 = ₹18,000.
(b) The policyholder bears the first ₹5,000 of each loss, so they still lose money from every claim. This gives a reason to drive carefully and not to make small or inflated claims, so both care and claim honesty improve.

Answer: Payments are ₹0, ₹3,000 and ₹15,000, total ₹18,000. The deductible keeps part of each loss with the policyholder, which reduces moral hazard.

Exam tips

Always state the timing (before or after the contract) in the first line. Examiners look for this distinction.
Match each control to the right problem and say why it works. A list of tools with no reasoning scores poorly.
For numeric parts, write the payment formula first, then substitute. Show the floor at zero for deductibles.
State assumptions, such as a fixed mix of risks or no expenses, whenever you calculate a fair premium.
Link to utility theory where asked: full cover at a fair price removes incentives to take care, while partial cover restores them.

Practice questions from Role of insurance in reducing or removing risk