IAI Actuarial Core Principles · Economic Modelling · Role of insurance in reducing or removing risk
For an individual with utility U(w), the Arrow-Pratt coefficient of absolute risk aversion is defined as which of the following?
The coefficient of absolute risk aversion is minus the second derivative of utility divided by the first derivative, −U''(w)/U'(w). It is positive for risk-averse individuals; multiplying by wealth w gives relative risk aversion instead.
- AU''(w)/U'(w)
- B−U''(w)/U'(w)Correct
- C−wU''(w)/U'(w)
- D−U'(w)/U''(w)
- U'(w)/U(w)
Explanation
Absolute risk aversion is A(w) = −U''(w)/U'(w), positive for concave utility. Option 2 without the minus sign is negative for risk-averse people. The version multiplied by w is relative risk aversion.
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