Utility and Portfolio Choice

Integrating twice gives for you show this w z exp

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Unformatted text preview: led the Arrow-Pratt absolute risk-aversion function ′(W ) 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 as risk-neutral • Quadratic utility function b u(x ) = x − x 2 , 2 rA (x ) =...
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This document was uploaded on 02/17/2014 for the course COURANT G63.2751.0 at NYU.

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