Unformatted text preview: u represents % . For all α ∈ ( 0, 1 ) and for all x , y ∈ Z , we have by risk aversion [ α x + ( 1 − α) y ] % α x ⊕ ( 1 − α) y and thus u (α x + ( 1 − α) y ) ≥ α u ( x ) + ( 1 − α) u ( y ) , that is, u is concave. Certainty Equivalence and the Risk Premium Let E ( p ) be the expectation of the lottery p , that is, E ( p ) = ∑ z ∈ Z p ( z ) z . Given a preference relation % over the space L ( Z ) , the certainty equiv-alence of a lottery p , CE ( p ) , is a prize satisfying [ CE ( p ) ] ∼ p . (To justify the existence of CE ( p ) we need to assume that % is monotonic and continuous in the sense that if p Â q , the inequality is maintained if we change both lotteries’ probabilities and prizes a “little bit”). The...
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- Fall '10
- Utility, Convex function, Concave function, Jensen's inequality, Jensen Inequality