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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