Risk, Insurance and Pooling
Insurance shares the cost of covered losses across a pool. Premiums help fund claims and running costs, while reserves help with uncertain payouts. Pooling works best when losses do not all happen together. Hidden risk differences can affect who buys cover and the price of the remaining pool.
What a learner can do afterwards
- Estimate an expected cost from a probability and a size of loss, and compare it with a quoted premium
- Explain how pooling many independent losses makes average claims per member more predictable, and why a shared disaster can still strain a pool
- Describe how hidden risk differences can attract higher-risk buyers to voluntary cover and raise expected claims per member
1 · Read
Expected loss is an average, not everyone's bill. Suppose a machine has a 1 in 100 chance of an 8,000-coin loss over one year, and otherwise loses nothing. Multiply probability by loss: 1/100 × 8,000 = 80 coins for that year. The actual loss is zero or 8,000. A premium is the price paid for insurance cover.
A commercial premium usually funds expected covered claims, running costs and a margin for uncertainty and profit. Investment income can also help pay costs. Expected claims of 80 coins and a premium of 115 leave a difference of 35. This does not guarantee payment of claims. With the same cover, higher expected claims may mean a higher price. Age can indicate group risk without predicting one driver's outcome.
Pooling uses many premiums to pay members' covered losses. Independent losses do not change one another's chances. With many similar independent risks, average claims per member become more predictable. Total claims still vary. One flood can damage many nearby homes, so adding homes in that flood zone does not remove the shared risk.
Adverse selection can arise when buyers know more about their risk than the insurer. At a shared price, people expecting larger claims may be more willing to buy voluntary cover. If lower-risk members leave, expected claims per remaining member rise. Higher premiums may prompt more departures. This can happen without anyone changing their own behavior.
A per-claim deductible is the first part of a covered loss you pay. With a 250-coin deductible and a 1,000-coin bill, the insurer pays 750 if no other limits apply. Higher deductibles often lower premiums. Cover may also reduce care taken to prevent theft. This behavior change is moral hazard. Sharing costs can reduce that incentive.
Expected loss is probability times loss. Pooling spreads covered costs, but shared disasters and hidden risk still matter. Check premiums, deductibles and limits.
Lesson, questions and flashcards written for this dataset.
Readings and flashcards written for this dataset. Linked video: "Term life insurance and death probability", Khan Academy.
More to read
An average loss is not an annual bill
A workshop considers three possible outcomes for one machine over a year. There is a 2% chance of a 2,000-coin repair, a 1% chance of a 9,000-coin replacement, and otherwise no loss. These outcomes cannot happen together in this example.
Expected loss is 0.02 × 2,000 + 0.01 × 9,000 = 40 + 90 = 130 coins. The no-loss outcome adds zero. This is an average across comparable cases, not a prediction of a 130-coin bill for this machine.
A policy may leave some costs with the workshop. A deductible, excluded cause or payout limit can reduce the amount paid by the insurer. When judging a premium, distinguish the full possible loss from the part the policy covers.
When many claims arrive together
Two pools can insure the same number of homes yet face different uncertainty. One covers homes spread across places with largely independent losses. The other covers homes beside the same river. One flood may damage many homes in the second pool.
Pool size alone does not show how safe a fund is. Loss probabilities, loss sizes and links between losses all matter. Independent risks help make average claims per member more predictable as a pool grows. They do not make total payouts identical every year.
Reserves and exposure spread across different risks can help an insurer meet claims. These measures do not promise payment for every disaster. Policy terms still determine which losses and amounts are covered.
Separate the premium from the claim payment
Rina pays a yearly premium of 180 coins for equipment cover. Her policy has a 300-coin deductible for each covered claim. A covered repair costs 1,200 coins. Assume the payout limit is high enough and no other charges apply.
Rina pays the first 300 coins of the repair. The insurer pays 1,200 - 300 = 900 coins. The premium is a separate payment for having cover, not a deduction from the repair bill. Rina pays it even in a year with no claim.
When comparing policies, check covered causes, deductibles, payout limits and claim conditions. A lower premium may leave more costs with the policyholder. Some insurance pays a stated benefit instead of reimbursing a bill, so this example does not describe every policy.
Hidden risk and changed behavior
A delivery company knows one route has frequent thefts. Its insurer cannot distinguish that route from safer routes and offers the same price for each. The company may be especially willing to insure the risky route. This illustrates adverse selection: buyers' information affects which risks enter a pool.
Now suppose an insured company stops securing its equipment because it expects payment after a theft. Cover has changed its behavior. This illustrates moral hazard.
Adverse selection concerns which buyers choose cover when risk is hidden. Moral hazard concerns behavior under cover. Neither means every buyer acts this way. Deductibles, prevention requirements and better information can change incentives, but their effects depend on the situation.
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