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IAI Actuarial Core Principles · Economic Modelling · Role of insurance in reducing or removing risk

A risk-averse individual with concave utility faces a random loss and can buy full insurance at a premium equal to the expected loss. Which statement follows from expected utility theory?

The individual prefers full insurance. For concave utility, Jensen's inequality gives that the utility of expected wealth exceeds the expected utility of random wealth. A fair premium leaves certain wealth equal to expected wealth, so the risk-averse person is better off insured.

  1. AThe individual prefers full insurance, because utility of the certain wealth exceeds expected utility of the uncertain wealthCorrect
  2. BThe individual is indifferent, since the expected wealth is the same
  3. CThe individual prefers no insurance, because expected utility is higher when risk is retained
  4. DThe individual prefers insurance only if utility is linear
  5. The individual prefers insurance only if the loss is certain

Explanation

By Jensen's inequality, for concave U, U(E[W]) > E[U(W)] when W is random. A fair premium gives certain wealth E[W], so full insurance gives higher expected utility. Linear utility would give indifference, which is risk neutrality, not risk aversion.

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