Lecture9 - Lecture 9 Risk aversion; risk premia, insurance...

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Lecture 9 Risk aversion; risk premia, insurance markets
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Definitions Expected value of outcomes X = {X 1 , X 2 , …, X n } with associated probabilities p(X 1 ), … , p(X n ) is E(X) = p(X 1 )X 1 + … p(X n )X n Expected utility: E(U(X)) = p(X 1 )U(X 1 )+p(X 2 )U(X 2 )+. .+ p(X n )U(X n )
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Risk Aversion Income is 1 million with probability ½ and 100,000 with probability ½. Expected income = (1,000,000)(.5) + (100,000)(.5) = 550,000 Expected utility = U(1M)(.5) + U(100K)(.5) Risk aversion: utility of expected income is larger than expected utility. income Utility 1 million 100,000 550,000 U(550K) E(U(X)) = .5U(1M)+ .5U(100K) Utility of Expected income = U[(.5)(1M)+(.5)(100K)] =U(550K)
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Risk preferences: utility for income Risk loving Risk averse Risk neutral A A A B B B
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Risk Premium The risk premium measures the income a risk averse person will give up in order to replace a risky outcome with a guaranteed outcome. The extent of risk aversion depends on the curvature of the utility
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This note was uploaded on 01/17/2012 for the course ECON 100A taught by Professor Safarzadeh during the Fall '09 term at UC Irvine.

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Lecture9 - Lecture 9 Risk aversion; risk premia, insurance...

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