Lesson preview · Risk Aversion
Insurance
~5 min · Free to read
Insurance is the practical application of risk aversion. A risk-averse person is willing to pay a premium to eliminate uncertainty. An insurance company, by pooling many independent risks, can predict its total payouts accurately (the law of large numbers). The insurer charges a premium at or above the actuarially fair level (expected loss) and makes a profit from the difference — while the insured gains peace of mind.
Key Term
Insurance Concepts
- Actuarially fair premium: , where is the probability of loss and is the loss amount.
- Maximum willingness to pay: The risk premium determines the maximum extra amount (above fair premium) the person will pay. Max premium .
- Law of large numbers: With many independent policyholders, the insurer’s average payout converges to the expected loss, making the business viable.
- Loading factor: Actual premiums exceed the fair premium by an amount covering administrative costs and profit.
A risk-averse person will pay up to to insure fully; this exceeds the fair premium by the risk premium
The trade is symmetric: the insured pays for certainty (risk premium), and the insurer provides certainty by pooling risk. With enough policyholders, the insurer’s risk is negligible (law of large numbers), so it’s nearly risk-neutral. This mutually beneficial trade is possible precisely because the insured is risk-averse: they value the certain outcome more than the gamble, even after paying a premium above the fair price.
Worked Example
A homeowner with has wealth 100,000 dollars. There’s a 2% chance of a 50,000 dollar fire loss. Find: (a) the actuarially fair premium, (b) the maximum they’d pay for full insurance.
Check yourself · no marks
Why can insurance companies afford to take on the risk that individuals want to avoid?
Commit to one first. Guessing and being wrong beats reading the answer cold.
Practice · 1 / 4
An actuarially fair insurance premium equals:
Next
Like what you read?
Sign up free to save your progress, get spaced reviews tuned to you, and unlock all 50 microeconomics knowledge points with interactive graphs and adaptive practice.