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IAI Actuarial Core Principles · Economic Modelling · Rational choice theory and utility

An investor has utility U(w) = -e^(-0.0002w). Her absolute risk aversion A(w) = -U''(w)/U'(w) is what?

Absolute risk aversion is the constant 0.0002. Differentiating gives U' = 0.0002e^(-0.0002w) and U'' = -(0.0002)^2 e^(-0.0002w), so -U''/U' = 0.0002 for every wealth level, the defining feature of exponential utility.

  1. A0.0002 at all wealth levelsCorrect
  2. B0.0002w
  3. C0.0002/w
  4. DDecreasing in w
  5. Equal to 1/w

Explanation

U' = 0.0002e^(-0.0002w), U'' = -0.0002^2 e^(-0.0002w). Ratio gives A(w) = 0.0002, constant. This is exponential utility with constant absolute risk aversion.

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