Slides19-2010 - Eliciting Risk Aversion Coecients: Lecture...

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Eliciting Risk Aversion Coefficients: Lecture XIX Charles B. Moss October 7, 2010 Charles B. Moss () Eliciting Risk Aversion Coefficients October 7, 2010 1 / 17
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1 Eliciting Risk Aversion Coefficients Direct Elicitation of Utility Functions Equally Likely Risky Prospect 2 Savage State-Dependent Expected Utility Charles B. Moss () Eliciting Risk Aversion Coefficients October 7, 2010 2 / 17
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Direct Elicitation of Utility Functions Assume two possible outcomes of a random variable Y 1 which occurs with probability p and Y 2 which occurs with probability 1 P . As the decision maker whether he prefers the risky alternative to a certain payoF ˜ Y . I Suppose the decision maker is given an alternative between a 50/50 bet of paying $50 or $5 (with the expected return of $27.50) or a certain payoF of $25. I If the decision maker choose the risky alternative, the decision maker’s risk aversion coefficient is less than 0.005944 E [ U ( Y )] = exp ( ρ Y 1 ) p exp ( ρ Y 2 )(1 p ) = exp ρ ˜ Y (1) Charles B. Moss () Eliciting Risk Aversion Coefficients October 7, 2010 3 / 17
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Continued I The value for ρ can be solved using Gauss-Seidel. exp ( ρ 26 . 0) 0 . 50 exp( ρ 5) 0 . 50 exp ( ρ 50) = 0 . (2) Charles B. Moss () Eliciting Risk Aversion Coefficients October 7, 2010 4 / 17
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If the answer is no (they prefer the certain outcome to the risky alternative), either I Change the probabilities by making the higher return more likely (i.e., let p =0 . 40), exp ( ρ 26 . 0) 0 . 40 exp( ρ 5) 0 . 60 exp( ρ 50) = 0 (3) for which the risk aversion coefficient increases to 0.0113. I Alternatively, decrease the certainty equivalent (i.e., to $25.75). Charles B. Moss () Eliciting Risk Aversion Coefficients October 7, 2010 5 / 17
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Equally Likely Risky Prospect and Finding its Certainty Equivalent (ELCE) This process begins by assigning the expected utility at two endpoint outcomes.
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Slides19-2010 - Eliciting Risk Aversion Coecients: Lecture...

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