week 11 B - COMM 295 Decision Making with Uncertainty Part...

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COMM 295 November 18, 2010 Decision Making with Uncertainty: Part 2
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Topics Insurance Diversification Behavioural peculiarities Prospect theory
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Risk Aversion
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Insurance Example Suppose U(X) = X 0.5 You face a 10% chance of disability Income with & without disability is 1 & 9 Disability insurance pays you 8 in the event of an accident (brings income to 9) Insurance company expects to pay you: Expected Claim = 0.1(8) = 0.8 What are you willing to pay for insurance?
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Insurance Example, Cont’n Risk Neutral Person Let C be cost of insurance Without insurance, expected income is 0.9(9) + 0.1(1) = 8.2 With insurance (guaranteed income = 9) expected income = 9 C Most a risk-neutral will pay for insurance is C RN = 0.8 (obtained by solving 9 C = 8.2) Notice that C RN = Expected Claim
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Insurance Example, Cont’n Risk Averse Person Without insurance, a risk averse person has expected utility: .9(9 .5 ) + .1(1 .5 ) With insurance (guarantees income = 9) expected utility is (9 C) .5 Indifferent when C = 1.16 because .9(9 .5 ) + .1(1 .5 ) = (9 1.16) .5 Maximum risk averse person will pay for insurance is 1.16
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