关于跨期消费与资产选择

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?
这是题目了，本来是觉得从期望单方面解决就可以了，但是后来想想不大对啊，求大牛解答之！

我自己解是解出来了，但是我不确定我连续概率下的VNM效用函数是不是正确，因为我找不到类似的例子，研究了好几个小时，在参考了MWG和其他的一些资料和书之后，自己编了一个，把答案勉强解了一下，可是发现用我自己的公式当证券种类趋向于无穷的时候，计算几乎变为不可能，虽然能根据方差的变化知道答案！╮(╯▽╰)╭，巨囧！这都什么题目啊，给我们本科生做这种题目！

同一道题。。。。 纠结啊