t*******y
发帖数: 637 | 1 you are given $100 now and are supposed to give back 100+a*max(I-100, 0)
after 1 year. what's the maximum value of a you can accept?
I is normal with mean 100, var \sigma^2, and int rate is r=6%.
是一道老题 感觉以前人给的答案不对 | d*********n
发帖数: 27 | 2 With the $100 given, you can invest and have $100 * e^r a year later risk
free;you do not gain anything if this is smaller than 100+a*max(I-100, 0).
Now E[max(I-100,0)] =integrate
{
(I-100)/sqrt(2pi*sigma^2)*exp[-(I-100)^2/2sigma^2]
, I=100
, I=+infinity
}
=\sigma*[1-phi(0)]
=0.5*sigma
Hence you want 100*e^r =100(1+r) > 100+a*0.5*sigma.
So a < 200*r/sigma
如果这跟前人的答案一样，那我也没办法了
【在 t*******y 的大作中提到】
: you are given $100 now and are supposed to give back 100+a*max(I-100, 0)
: after 1 year. what's the maximum value of a you can accept?
: I is normal with mean 100, var \sigma^2, and int rate is r=6%.
: 是一道老题 感觉以前人给的答案不对
| t*******y
发帖数: 637 | 3 积分好像积错了吧
我积出来是 \sigma/sqrt(2*pi)
【在 d*********n 的大作中提到】
: With the $100 given, you can invest and have $100 * e^r a year later risk
: free;you do not gain anything if this is smaller than 100+a*max(I-100, 0).
: Now E[max(I-100,0)] =integrate
: {
: (I-100)/sqrt(2pi*sigma^2)*exp[-(I-100)^2/2sigma^2]
: , I=100
: , I=+infinity
: }
: =\sigma*[1-phi(0)]
: =0.5*sigma
| p********2
发帖数: 9939 | 4 嗯，我ji了一下，和你一样
【在 t*******y 的大作中提到】
: 积分好像积错了吧
: 我积出来是 \sigma/sqrt(2*pi)
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