# The result follows exercise 627 exercise mean

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The result follows. Exercise 6.27 (exercise: mean-variance). Suppose a consumer’s utility for a CDF is U ( F ) = μ F α Var( F ), where Var( F ) = integraldisplay ( x μ F ) 2 dF is the variance of F . 1. Prove that if α > α then the preference corresponding to α is more risk averse than that corresponding to α .
2. Prove that U violates expected utility.
Section 6: vNM Representation Theorem and Risk 6-23 Exercise 6.31 (12.12). Prove the following proposition: Suppose followsorequal is represented by a twice continuously differentiable vNM index v . Then followsorequal exhibits constant ab- solute risk aversion if and only if there exists a > 0 and b R such that either v ( x ) = ax + b for all x or v ( x ) = ae λx + b for all x . This is sometimes called the CARA utility index for wealth.