Unformatted text preview: Problem 3. ( Standard ) Consider a consumer’s preference over K-tuples of K uncertain assets. De-note the random return on the k th asset by Z k . Assume that the random variables ( Z 1 , . . . , Z K ) are independent and take positive values with proba-bility 1. If the consumer buys the combination of assets ( x 1 , . . . , x K ) and if the vector of realized returns is ( z 1 , . . . , z K ) , then the consumer’s total wealth is ∑ K k = 1 z k x k . Assume that the consumer satisFes vNM assumptions, that is, there is a function v (over the sum of his returns) so that he maximizes the expected value of v . Assume that v is increasing and concave. The con-sumer preferences over the space of the lotteries induce preferences on the space of investments. Show that the induced preferences are monotonic and convex....
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- Fall '10
- Utility, Probability theory, Convex function, Slovic