Lecture20-2004 - Generalized Stochastic Dominance with Respect to a Function Lecture XX I Meyer Jack Choice among Distributions Journal of Economic

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1 Generalized Stochastic Dominance with Respect to a Function Lecture XX I. Meyer, Jack “Choice among Distributions.” Journal of Economic Theory 14(1977): 326-36. A. The general idea of the manuscript is to restrict the risk aversion coefficient for stochastic dominance to those risk aversion coefficients in a given interval () () () 12 rx rx rx << . B. This problem will be solved by finding the utility function () ux which satisfies: rx x 01 ''( ) '( ) [,] ≤− ∀ ∈ and minimizes [] Gx Fx u xd x () ' 0 1 1. Given that this integral yields the expected value of Fx minus the expected value of ( ) , the minimum will be greater than zero if is preferred to ( ) by all agents who prefer to ( ) . 2. If the minimum is less than zero, then the preference is not unanimous for all agents whose risk aversion coefficients are in the state range. 3. Another problem is that utility is invariant to a linear tranposition. Thus, we must stipulate that ( ) u = . C. The problem is then to use the control variable ( ) ′′ to maximize the objective function −− x 0 1 subject to the equation of motion '( ) ' =− and the control constraints +≥ 1 2 0 0 with the initial condition ( ) u = . 1. Rewriting the problem, substituting ( ) zx yields
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AEB 6182–Agricultural Risk Analysis and Decision Making Fall 2004 Professor Charles Moss Lecture 20 2 [] () max ( ) ( ) '( ) '( ) ' '( ) ( ) −− = −+ −≤ Gx Fx u xd x st u x u x z x zx
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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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Lecture20-2004 - Generalized Stochastic Dominance with Respect to a Function Lecture XX I Meyer Jack Choice among Distributions Journal of Economic

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