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Lecture34-2004

# Lecture34-2004 - Lecture XXXIV Constant Relative and...

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1 Lecture XXXIV Constant Relative and Absolute Risk Aversion and Derivation of the State Contingent Dual Functions I. Constant Relative and Absolute Risk Aversion A. Risk Premium: 1. Based on the definition of risk aversion from the preceding lecture, Chambers and Quiggin define the Risk Premium as the amount that a risk averse decision maker is willing to sacrifice to obtain a certain payoff. 45 0 Fair-Odds Line A 2 y 1 y 1 2 π π y * y 2. In this graph y is an outcome from a state-contingent output combination , however given risk aversion, the decision maker is indifferent between the state-contingent output combination * y and y . Note that * y is a certain payoff because it is on the 45 0 line. a. The certainty equivalent is the distance between point y and point * y in state-space. b. Analytically, the absolute risk premium is defined by the benefit function: ( ) ( ) ( ) ( ) { } ( ) ( ) max : 1 , 1 r y c W y c W y B W y y = = 3. The relative risk premium is then defined by the distance function:

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AEB 6182–Agricultural Risk Analysis and Decision Making Lecture 34 Professor Charles Moss Fall 2004
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• Fall '08
• Weldon
• absolute risk aversion, Professor Charles Moss, AEB 6182–Agricultural Risk, 6182–Agricultural Risk Analysis

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Lecture34-2004 - Lecture XXXIV Constant Relative and...

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