IAI Actuarial Core Principles · Economic Modelling · Rational choice theory and utility
An investor has utility U(w) = -e^(-0.02w), with w in Rs lakh. What is her coefficient of absolute risk aversion and how does it change as wealth rises?
Absolute risk aversion is 0.02 and constant. Dividing minus the second derivative by the first derivative cancels the exponential term, leaving 0.02 regardless of wealth. This is the defining feature of exponential utility, whereas log utility has absolute risk aversion of 1/w, which falls with wealth.
- A0.02, constantCorrect
- B0.02w, increasing
- C0.02, decreasing
- D1/w, decreasing
- 0.02, increasing
Explanation
U'(w) = 0.02e^(-0.02w) and U''(w) = -0.0004e^(-0.02w). Absolute risk aversion = -U''/U' = 0.02, which does not depend on w. The exponential utility therefore shows constant absolute risk aversion. The 1/w form belongs to log utility.
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