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Unformatted text preview: led the Arrow-Pratt absolute risk-aversion function
u This measure incorporates everything important in a utility function but is free
from arbitrary scaling factors
• We can recover the utility function from rA by using that rA (W ) = −d[log u ′(W )] / dW . Integrating twice gives (For you: show this) ∫ W z
exp ⎢−∫ rA (x )dx ⎥ dz = a + bu(W )
⎣⎢ with b > 0 RISK AND PORTFOLIO MANAGEMENT WITH ECONOMETRICS, VER. 10/23/2012. © P. KOLM. 9 It is common also to talk about the Arrow-Pratt relative risk aversion, defined by
rR (W ) = − Wu ′′(W )
u ′(W ) RISK AND PORTFOLIO MANAGEMENT WITH ECONOMETRICS, VER. 10/23/2012. © P. KOLM. 10 Some Common Utility Functions RISK AND PORTFOLIO MANAGEMENT WITH ECONOMETRICS, VER. 10/23/2012. © P. KOLM. 11 • Linear utility function
u(x ) = a + bx , rA (x ) = rR (x ) = 0 The risk aversions are zero and therefore the linear utility function is referred to
• Quadratic utility function b
u(x ) = x − x 2 ,
rA (x ) =...
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This document was uploaded on 02/17/2014 for the course COURANT G63.2751.0 at NYU.
- Fall '14