Lecture19-2010 - Eliciting Risk Aversion Coecients: Lecture...

Info iconThis preview shows pages 1–3. Sign up to view the full content.

View Full Document Right Arrow Icon
Eliciting Risk Aversion Coefficients: Lecture XIX Charles B. Moss October 7, 2010 I. Eliciting Risk Aversion Coefficients A. Direct Elicitation of Utility Functions 1. Assume two possible outcomes of a random variable Y 1 which occurs with probability p and Y 2 which occurs with probability 1 P . 2. As the decision maker whether he prefers the risky alternative to a certain payo± ˜ Y . a) Suppose the decision maker is given an alternative be- tween a 50/50 bet of paying $50 or $5 (with the expected return of $27.50) or a certain payo± of $25. b) If the decision maker choose the risky alternative, the de- cision maker’s risk aversion coefficient is less than 0.005944 E[ U ( Y )] = exp ( ρY 1 ) p exp ( ρY 2 )(1 p )= exp ρ ˜ Y (1) c) 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) 2. If the answer is no (they prefer the certain outcome to the risky alternative), either 1
Background image of page 1

Info iconThis preview has intentionally blurred sections. Sign up to view the full version.

View Full DocumentRight Arrow Icon
AEB 6182 Agricultural Risk Analysis and Decision Making Professor Charles B. Moss Lecture XIX Fall 2010 a) 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. b) Alternatively, decrease the certainty equivalent (i.e., to $25.75). B. Equally Likely Risky Prospect and Finding its Certainty Equiva- lent (ELCE) 1. This process begins by assigning the expected utility at two endpoint outcomes. a) Consider a low income of $50,000 ( a =50 , 000) and a high income of $100,000 ( b = 100 , 000). b) Next, assign a utility value at each endpoint ( U (50 , 000) = U ( a )=0and U (100 , 000) = U ( b )=1) . 2. The research then asks the decision maker how much they would be willing to give or take (or what is the certainty equivalent) for a gamble paying $50,000 with probability 0.50 and $100,000 with probability 0.5.
Background image of page 2
Image of page 3
This is the end of the preview. Sign up to access the rest of the document.

This note was uploaded on 07/15/2011 for the course AEB 6182 taught by Professor Weldon during the Fall '08 term at University of Florida.

Page1 / 6

Lecture19-2010 - Eliciting Risk Aversion Coecients: Lecture...

This preview shows document pages 1 - 3. Sign up to view the full document.

View Full Document Right Arrow Icon
Ask a homework question - tutors are online