IAI Actuarial Core Principles · Economic Modelling · Rational choice theory and utility
An investor has utility U(w) = -e^(-0.0001w), with w in rupees. What is the coefficient of absolute risk aversion at wealth Rs 5,00,000, and how does it vary with wealth?
Absolute risk aversion is 0.0001 and does not change with wealth. Dividing minus the second derivative by the first derivative of the exponential utility cancels the wealth term, so it exhibits constant absolute risk aversion.
- A0.0001 at Rs 5,00,000; constant in wealthCorrect
- B0.0001 at Rs 5,00,000; decreasing in wealth
- C50 at Rs 5,00,000; increasing in wealth
- D0.0001 at Rs 5,00,000; increasing in wealth
- 0.00002 at Rs 5,00,000; constant in wealth
Explanation
U' = 0.0001e^(-0.0001w) and U'' = -(0.0001)^2 e^(-0.0001w). A(w) = -U''/U' = 0.0001, independent of w. This is the exponential utility, which has constant absolute risk aversion. Wealth level is irrelevant to A(w).
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