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Security A pays $ 100 for sure at the end of the year and costs $95 now. Security B has a uniform distribution of payout on the interval [80,120]. Your utility function for wealth is
U(x)=-1/x, and your initial wealth is $100. You have no relevant consumption needs between now
and the end of the year (i.e., you are not limited in how much of your wealth you can invest). You can buy any real number of units of any security, i.e., you are not limited to a whole number of units.

a)
if the security A and B are the only investments available, what is the maximum price of security B at which you would be willing to buy?
b)
Suppose there also exists security C, described by the same distribution as security B, and the payouts of the B and C are independent ( and hence uncorrelated). What would now be the maximum prices of security B and C at which you would be willing to buy them?
c) now suppose that there are infinitely many security B1, B2, B3, ……, which all have the same distribution as security B. At what price would you buy them if they are all mutually independent? Why if they are all positively correlated, and the coefficient of correlation between any two of them is 0.2?

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关键词：金融经济 distribution Independent coefficient correlation 经济 金融 帮忙 高人

一个疑问是财富的效用函数居然能是负的吗？
a）的解答在于衡量资产A和资产B价格和年末资产效用，两者相等就可求出B的价格。
b）和c）我暂时还想不出思路来，请其他会员帮忙吧！

算期望就可以了！其实很简单的