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eco331-08-StochasticDominanceHandout

# eco331-08-StochasticDominanceHandout - Overview First-Order...

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Overview First-Order Stochastic Dominance Second-Order Stochastic Dominance Eco331: Stochastic Dominance Marciano Siniscalchi November 1, 2009

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Overview First-Order Stochastic Dominance Second-Order Stochastic Dominance Overview Can we make predictions with P but without u ? First-Order Stochastic Dominance Characterization: FOSD = preferred by all strictly increasing u Second-Order Stochastic Dominance Characterization: SOSD = preferred by all strictly increasing and concave u .
Overview First-Order Stochastic Dominance Second-Order Stochastic Dominance The Basic Idea High probability of high payoﬀs is good. Deﬁnition For any two random variables X , Y , say that X ﬁrst-order stochastically dominates Y (or X FOSD Y ) iﬀ, for all m R , Pr[ X > m ] Pr[ Y > m ] . Note: transitive but partial order.

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First-Order Stochastic Dominance Second-Order Stochastic Dominance An Example X : (10 , 1 2 ; 5 , 1 2 ) Y : (10 , 1 3 ; 6 , 1 6 ; 3 , 1 2 ). For m < 3, Pr[ X > m ] = Pr[ Y > m ] = 1; for 3 m < 5, Pr[ X > m ] = 1 > Pr[ Y > m ] = 1 2 ; for 5 m < 6, Pr[ X > m ] = Pr[ Y > m ] = 1 2 ; for 6 m < 10, Pr[ X > m ] = 1 2 > Pr[ Y > m ] = 1 3 ; and for m 10, Pr[ X > m ] = Pr[ Y > m ] = 0. So,
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eco331-08-StochasticDominanceHandout - Overview First-Order...

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