eco331-07-ArrowPrattHandout

eco331-07-ArrowPrattHandout - Overview Risk Premium Eco331:...

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Unformatted text preview: Overview Risk Premium Eco331: The Arrow-Pratt Measure(s) of Risk Aversion Marciano Siniscalchi October 21, 2009 Overview Risk Premium Overview Risk Premium Characterizing Risk Aversion via Risk Premia The Arrow-Pratt measure and Risk Premia Overview Risk Premium The Basic Idea Recall this example: Suppose we roll a die. If 1 , 2 , 3 , 4: you win $5,000 . If 5 , 6: you lose $5,000 . Would you take this bet? Now suppose I win NSF grant, give you $10,000,000. Would you take the bet now? We need a localized notion of risk aversion. Overview Risk Premium Risk Premium: Turning Things Upside Down Suppose by default, you must bear a risk A risk is a lottery with E = 0. Initial wealth W , terminal wealth W + If risk-averse: W W + . Now ask: what price to avoid playing the lottery? The answer in general depends upon W . Definition Consider a r.v. with E = 0, and a DM with strictly increasing, continuous Bernoulli utility u and wealth W . The risk premium the DM is willing to pay to avoid the risk at wealth level...
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eco331-07-ArrowPrattHandout - Overview Risk Premium Eco331:...

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