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# ecg590i_lecture08 - ECG590I Asset Pricing Lecture 8 Risk...

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ECG590I Asset Pricing. Lecture 8: Risk Aversion 1 8 Risk Aversion 8.1 Utility 1. Simple case Utility (happiness) depends on consumption More consumption always raises utility OK for total consumption There are exceptions for particular goods (example: sun bathing) The increase in utility brought about by a given increase in consumption is smaller the more consumption you already have. John Seater, North Carolina State University, Fall 2007

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ECG590I Asset Pricing. Lecture 8: Risk Aversion 2 2. Mathematical representation Utility function: U = U ( C ) Marginal utility: dU dC = U 0 ( C ) > 0 Diminishing marginal utility: d 2 U dC 2 < 0 These properties imply that the utility is a concave function John Seater, North Carolina State University, Fall 2007
ECG590I Asset Pricing. Lecture 8: Risk Aversion 3 John Seater, North Carolina State University, Fall 2007

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4 8.2 Risk aversion 8.2.1 Basic intuition Consider a simple lottery where you have a probability p of winning C ± 1 and probability q = 1 ± p of winning C + 1 . Suppose p = 0 : 5 . The expected monetary gain from the lottery is E [ C ] = 0 : 5( C ± 1) + 0 : 5( C + 1) = C The expected utility from the lottery is E [ U ] = 0 : 5 U ( C ± 1) + 0 : 5 U ( C + 1) < U ( E [ C ]) (
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• Fall '08
• msmorril
• North Carolina State University, North Carolina State, Carolina State University, John Seater, ECG590I Asset Pricing

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ecg590i_lecture08 - ECG590I Asset Pricing Lecture 8 Risk...

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