Slides18-2010 - Risk Aversion Coecients and Transfor-...

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Unformatted text preview: Risk Aversion Coecients and Transfor- mations Charles B. Moss Outline Arrow-Pratt Coecients for particular functions Quadratic Utility Function Power Utility Function Negative Exponential Utility Hyperbolic Absolute Risk Aversion Interpretations and Transfor- mations Utility Functions, Risk Aversion Coecients and Transformations: Lecture XVIII Charles B. Moss October 5, 2010 Charles B. Moss Risk Aversion Coecients and Transformations Risk Aversion Coecients and Transfor- mations Charles B. Moss Outline Arrow-Pratt Coecients for particular functions Quadratic Utility Function Power Utility Function Negative Exponential Utility Hyperbolic Absolute Risk Aversion Interpretations and Transfor- mations 1 Arrow-Pratt Coecients for particular functions Quadratic Utility Function Power Utility Function Negative Exponential Utility Hyperbolic Absolute Risk Aversion 2 Interpretations and Transformations Charles B. Moss Risk Aversion Coecients and Transformations Risk Aversion Coecients and Transfor- mations Charles B. Moss Outline Arrow-Pratt Coecients for particular functions Quadratic Utility Function Power Utility Function Negative Exponential Utility Hyperbolic Absolute Risk Aversion Interpretations and Transfor- mations Arrow-Pratt Coecients for particular functions Quadratic Utility Function: To specify the appropriate shape of the utility function, the quadratic function becomes U ( w ) = aw bw 2 U ( w ) = a 2 bw U 00 ( w ) = 2 b (1) Arrow-Pratt absolute risk aversion coecient R A ( w ) = 2 b a 2 bw R A ( w ) = 2 b a 2 bw dR A ( w ) dw = 2 b 2 b ( a 2 bw ) 2 > d dx 1 f ( x ) = f ( x ) ( f ( w )) 2 (2) Charles B. Moss Risk Aversion Coecients and Transformations Risk Aversion Coecients and Transfor- mations Charles B. Moss Outline Arrow-Pratt Coecients for particular functions Quadratic Utility Function Power Utility Function Negative Exponential Utility Hyperbolic Absolute Risk Aversion Interpretations and Transfor- mations Arrow-Pratt relative risk aversion coecient R R ( w ) = 2 b a 2 bw w = 2 b a w 2 b dR R ( w ) dw = 2 b 2 b ( a 2 bw ) 2 + 2 b a 2 bw > (3) Charles B. Moss Risk Aversion Coecients and Transformations Risk Aversion Coecients and Transfor- mations Charles B. Moss Outline Arrow-Pratt Coecients for particular functions Quadratic Utility Function Power Utility Function Negative Exponential Utility Hyperbolic Absolute Risk Aversion Interpretations and Transfor- mations Power Utility Function U ( w ) = w 1 r 1 r U ( w ) = w r U 00 ( w ) = rw...
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Slides18-2010 - Risk Aversion Coecients and Transfor-...

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