B*****9
发帖数: 48 | 1 suppose current stock price is $60. the stock price follows a geometric
brownian motion with parameter (mu, sigma)what's the expected time that the
stock price hits 150? |
f*****s
发帖数: 141 | 2 ln(S_t/S_0) starts from zero, hit ln(150/160), use exponential martingale to
solve this. |
h*y
发帖数: 1289 | 3 why ln(150/160), typo?
to
【在 f*****s 的大作中提到】
: ln(S_t/S_0) starts from zero, hit ln(150/160), use exponential martingale to
: solve this.
|
f*****s
发帖数: 141 | 4 Seems the exponential martingale approach does not work, since P(hit 150) =
1.
Can we directly use E[S_t] = 60 * exp{mu t} = 150, then solve t?
|
B*****9
发帖数: 48 | 5 should be 60 * exp{(mu-sigma^2/2)t}?
if mu
=
?
【在 f*****s 的大作中提到】
: Seems the exponential martingale approach does not work, since P(hit 150) =
: 1.
: Can we directly use E[S_t] = 60 * exp{mu t} = 150, then solve t?
:
|
f*****s
发帖数: 141 | 6 Sorry, this GBM, E(S_t)=60exp(mu*t)=150 ==>t = 1/mu * log(150/60)
Is this correct? |
f*****s
发帖数: 141 | 7 Sorry, this GBM, E(S_t)=60exp(mu*t)=150 ==>t = 1/mu * log(150/60)
Is this correct? |
c**********s
发帖数: 295 | 8 log(GBM) is a BM with drift, then use change of measure and reflection. |
b**********5
发帖数: 51 | 9 I think we can use E[S_t] = 60 * exp{mu t} = 150, then solve t. See the
following linkage at Wiki:
http://en.wikipedia.org/wiki/Geometric_Brownian_motion |
M*****y
发帖数: 666 | 10 not agree.
it is one of stochastic process problems involving ODE method
the result is little complicated |
