楼主: guo604250291
457 0

[金融计量学] 跪求数学大佬帮忙解决个问题!!!!谢谢!!有关optimization的问题 [推广有奖]

  • 1关注
  • 0粉丝

本科生

6%

还不是VIP/贵宾

-

威望
0
论坛币
229 个
学术水平
0 点
热心指数
2 点
信用等级
0 点
经验
162 点
帖子
34
精华
0
在线时间
89 小时
注册时间
2015-7-7
最后登录
2018-9-20

guo604250291 发表于 2018-9-13 07:25:14 |显示全部楼层
30论坛币
There are n mutual funds and m asset categories. Let aij be the fraction of the capital of fund j invested in category i. We have initial capital C and we want to invest all or part of it in these funds. We denote by xj the amount invested in fund j = 1, . . . , n. No short selling is allowed, so xj has to be nonnegative.
  • (a)  Describe the set X Rn of all possible amounts invested in these funds (fund portfolios). What are its extreme points?
  • (b)  Describe the set Y Rm of all possible amounts invested in this way in the m asset categories (asset portfolios).
  • (c)  Show that if a point y is an extreme point of Y , it has the form y = Ax, where x is an extreme point of X.
  • (d)  Suppose y Y is an asset portfolio obtained by investing in some of the available funds. Prove that you can construct it by investing in no more than m + 1 funds.




您需要登录后才可以回帖 登录 | 我要注册

GMT+8, 2018-9-23 17:15