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October 22nd, 2015, 05:44 PM  #1 
Newbie Joined: Oct 2015 From: Cambridge United Kingdom Posts: 1 Thanks: 0  Risk aversion, certainty equivalence, stochastic dominance
Suppose an agent has von NeumannMorgenstern preferences over money lotteries that can be represented by the utility function: U(p) = Sum[p(x)u(x)], where u(x) = − exp(−λx) for some λ > 0. (a) Derive the agent’s coefficient of absolute risk aversion. Now suppose for this agent the certain equivalent of an equalodds (i.e., 50–50) gamble of winning $1,000 or winning nothing is $470. (b) What can you say about the certain equivalent of an equalodds gamble of winning $1,500 or winning $500? (c) Suppose this agent must choose between (i) $175 for sure; (ii) a gamble that will pay $0, $100, $350, or $1000 with probabilities 0.28, 0.5, 0.1, and 0.12, respectively; (iii) a gamble that is equally likely to pay $0, $100, $200, or $520; and (iv) a gamble that will pay $0, $100, $200, $400 or $1000 with probabilities 0.25, 0.35, 0.25, 0.05 and 0.1. i. Find the expected values of the lotteries. ii. Show that (iii) second order stochastically dominates (iv). iii. Show that (iv) second order stochastically dominates (ii). iv. Using that the certain equivalent of an equalodds (i.e., 50–50) gamble of winning $1,000 or winning nothing is $470, find a lottery such that the agent is indifferent between this lottery and receiving $175 for sure (hint: this lottery can involve the agent sometimes loosing money). v. Hence argue that the agent most prefers lottery (iii). I have answered (a), (b) and c(i) but left them there because they may help with the other parts. Any help would be great, thanks. 

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aversion, certainty, dominance, equivalence, risk, stochastic 
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