IAI Actuarial Core Principles · Business Management · Decision-making process, attitude to risk and competition
A Mumbai general insurer's chief risk officer notes that the company's shareholders can diversify across many holdings, whereas its policyholders each hold one policy against a major loss. Which conclusion about insurance demand best follows from utility theory?
Risk-averse policyholders can rationally pay a premium above the expected claim. Because their utility is concave, the certainty of insurance raises expected utility compared with bearing the loss risk. This gap is what makes commercial insurance viable.
- ARisk-averse policyholders may pay a premium above the expected claim because insurance raises their expected utilityCorrect
- BPolicyholders will buy insurance only if the premium is below the expected claim
- CInsurance has no value to a person with concave utility
- DInsurance is attractive only to risk-seeking individuals
- Policyholders with diminishing marginal utility will always refuse full cover
Explanation
With concave utility, the certain wealth after paying a premium can give higher utility than the expected utility of the uninsured risky position, even when the premium exceeds the expected claim. This margin lets the insurer cover costs and profit. The claim that they buy only below expected claim would make insurance unviable.
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