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

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Unformatted text preview: Risk Aversion Coefficients and Transfor- mations Charles B. Moss Outline Arrow-Pratt Coefficients for particular functions Quadratic Utility Function Power Utility Function Negative Exponential Utility Hyperbolic Absolute Risk Aversion Interpretations and Transfor- mations Utility Functions, Risk Aversion Coefficients and Transformations: Lecture XVIII Charles B. Moss October 5, 2010 Charles B. Moss Risk Aversion Coefficients and Transformations Risk Aversion Coefficients and Transfor- mations Charles B. Moss Outline Arrow-Pratt Coefficients for particular functions Quadratic Utility Function Power Utility Function Negative Exponential Utility Hyperbolic Absolute Risk Aversion Interpretations and Transfor- mations 1 Arrow-Pratt Coefficients 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 Coefficients and Transformations Risk Aversion Coefficients and Transfor- mations Charles B. Moss Outline Arrow-Pratt Coefficients for particular functions Quadratic Utility Function Power Utility Function Negative Exponential Utility Hyperbolic Absolute Risk Aversion Interpretations and Transfor- mations Arrow-Pratt Coefficients 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 coefficient 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 Coefficients and Transformations Risk Aversion Coefficients and Transfor- mations Charles B. Moss Outline Arrow-Pratt Coefficients 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 coefficient 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 Coefficients and Transformations Risk Aversion Coefficients and Transfor- mations Charles B. Moss Outline Arrow-Pratt Coefficients 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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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.

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

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