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

An individual has utility U(w) = 1 - e^(-0.01w) with w in rupees thousands. What are the absolute risk aversion A(w) = -U''(w)/U'(w) and the behaviour of A as wealth rises?

Absolute risk aversion is constant at 0.01. The first derivative is 0.01e^(-0.01w) and the second is -0.0001e^(-0.01w), so their ratio is 0.01 whatever the wealth. Exponential utility therefore exhibits constant absolute risk aversion.

  1. AA(w) = 0.01 for all w; constant absolute risk aversionCorrect
  2. BA(w) = 0.01w; increasing absolute risk aversion
  3. CA(w) = 1/w; decreasing absolute risk aversion
  4. DA(w) = 0.01/w; decreasing absolute risk aversion
  5. A(w) = 0.01e^(-0.01w); decreasing absolute risk aversion

Explanation

U' = 0.01e^(-0.01w), U'' = -0.0001e^(-0.01w). Therefore A = 0.0001/0.01 = 0.01, independent of w. This is the exponential (CARA) utility.

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