x********o
发帖数: 519 | 1 the interviewer told me that int_0^T |W_t|dW_t is not a martingale.
I am really confused. by the martingale representation theorem, it should be
a martingale.
where is wrong?
Thanks for any explanation in advance. |
J*****n
发帖数: 4859 | 2
be
Expectation is always increasing with time. Definitely not a martingale.
【在 x********o 的大作中提到】
: the interviewer told me that int_0^T |W_t|dW_t is not a martingale.
: I am really confused. by the martingale representation theorem, it should be
: a martingale.
: where is wrong?
: Thanks for any explanation in advance.
|
B******5
发帖数: 4676 | 3 I think it is,
maybe I am wrong...
【在 J*****n 的大作中提到】
:
: be
: Expectation is always increasing with time. Definitely not a martingale.
|
x********o
发帖数: 519 | 4 I think you may think of the variance.
【在 J*****n 的大作中提到】
:
: be
: Expectation is always increasing with time. Definitely not a martingale.
|
l****o
发帖数: 2909 | 5 这种题目都不会，回家好好看两个月书，再出来投简历。不是贬低你，没准备好就乱投
简历，很多好机会就浪费了。 |
d*j
发帖数: 13780 | 6 sigh .....
I wan dan le....
have no idea about almost all of those interview questions now |
x********o
发帖数: 519 | 7 well, first of all, I do not think all of the people on this board know the
answer,
maybe at least 50% of them do not know, just like me.
second, your reply just shows how arrogant you are, nothing else.
【在 l****o 的大作中提到】
: 这种题目都不会，回家好好看两个月书，再出来投简历。不是贬低你，没准备好就乱投
: 简历，很多好机会就浪费了。
|
n******m
发帖数: 169 | 8 I believe it is a martingale. |
x********o
发帖数: 519 | 9 That's what I thought. so the interviewer is wrong?
【在 n******m 的大作中提到】
: I believe it is a martingale.
|
L*****k
发帖数: 327 | 10 恩，这个可以看成是从0到W_t的路径长度吗？
be
【在 x********o 的大作中提到】
: the interviewer told me that int_0^T |W_t|dW_t is not a martingale.
: I am really confused. by the martingale representation theorem, it should be
: a martingale.
: where is wrong?
: Thanks for any explanation in advance.
|
|
|
n******m
发帖数: 169 | 11 长度是 dt 不是 dw
【在 L*****k 的大作中提到】
: 恩，这个可以看成是从0到W_t的路径长度吗？
:
: be
|
l*****y
发帖数: 317 | 12 If they reject you only because you couldn't figure out the problems, just
let it be. I'm pretty sure you would have a hard time getting adapted to the
atmosphere even if you were hired.
A lot of ppl were asking how to solve xxx after the interviews. Someone gave
you the answer, probably after a 1/2/5/10/30 min consideration. So what?
You are expecting the same questions or the ones you were fully prepared for
in the next interview? From my experience, that really has a low
probability. And if you couldn't figure out a single question within the
first minute, you have already left an impression to the interviewer that
you are not solid on that part. And based on the various background of the
interviewers, it's just so simple to get you into troubles.
I'm not saying you shouldn't ask questions, but I really don't like some ppl
who are always listing a bunch of questions on the board saying "oh, here
are the real interview questions. I can't do this this and this, you guys
please help me". Just think about it. You believe you would pass the
interviews just by being able to solve all these problems? If you could, you
probably wouldn't stay here just asking questions but going to a top-tier
bank to launch your career.
So my point is pretty straightforward: do whatever you can and drop whatever
you can't. Be cool!
the
【在 x********o 的大作中提到】
: well, first of all, I do not think all of the people on this board know the
: answer,
: maybe at least 50% of them do not know, just like me.
: second, your reply just shows how arrogant you are, nothing else.
|
c**********e
发帖数: 2007 | 13 Your idea is close, but expectation increases with time only when Wt is positive. The expection decreases if Wt is negative.
【在 J*****n 的大作中提到】
:
: be
: Expectation is always increasing with time. Definitely not a martingale.
|
n****e
发帖数: 629 | 14 You should counter the interviewer: is Wt^2 dWt a martingale? |
s**********y
发帖数: 353 | 15 LZ在 question面试的人。 贴一些题目挺好的，大家互相讨论，否则要这个版干嘛？
这应该是martingale.
the
gave
for
【在 l*****y 的大作中提到】
: If they reject you only because you couldn't figure out the problems, just
: let it be. I'm pretty sure you would have a hard time getting adapted to the
: atmosphere even if you were hired.
: A lot of ppl were asking how to solve xxx after the interviews. Someone gave
: you the answer, probably after a 1/2/5/10/30 min consideration. So what?
: You are expecting the same questions or the ones you were fully prepared for
: in the next interview? From my experience, that really has a low
: probability. And if you couldn't figure out a single question within the
: first minute, you have already left an impression to the interviewer that
: you are not solid on that part. And based on the various background of the
|
i**w
发帖数: 71 | 16 |W_t|是adapted process
也能找到一个simple process无限逼近|W_t|: 取|W(jT/n)|
所以这个Ito积分是有定义的
而且E{int_0^T |W_t|^2 dt} finite，所以应该是martingale
不知道这个interviewer是怎么想的。
//别被那些很negative的人和话影响，直接ignore.当然，实力才是硬道理。加油!
should be
【在 x********o 的大作中提到】
: the interviewer told me that int_0^T |W_t|dW_t is not a martingale.
: I am really confused. by the martingale representation theorem, it should be
: a martingale.
: where is wrong?
: Thanks for any explanation in advance.
|
s*******0
发帖数: 3461 | 17 麻烦 直接提供一下 你的思路
大家都是中国人 何必呢
【在 l****o 的大作中提到】
: 这种题目都不会，回家好好看两个月书，再出来投简历。不是贬低你，没准备好就乱投
: 简历，很多好机会就浪费了。
|
n******t
发帖数: 4406 | 18 To be honest, WTF are you talking about?
the
gave
for
【在 l*****y 的大作中提到】
: If they reject you only because you couldn't figure out the problems, just
: let it be. I'm pretty sure you would have a hard time getting adapted to the
: atmosphere even if you were hired.
: A lot of ppl were asking how to solve xxx after the interviews. Someone gave
: you the answer, probably after a 1/2/5/10/30 min consideration. So what?
: You are expecting the same questions or the ones you were fully prepared for
: in the next interview? From my experience, that really has a low
: probability. And if you couldn't figure out a single question within the
: first minute, you have already left an impression to the interviewer that
: you are not solid on that part. And based on the various background of the
|
l****o
发帖数: 2909 | 19 check the property of a special form of girsanov's SDE's solution.
【在 s*******0 的大作中提到】
: 麻烦 直接提供一下 你的思路
: 大家都是中国人 何必呢
|
M****i
发帖数: 58 | 20 I think that it is your interviewer should go home to go over the definition
of the stochastic integral. Remember that, at the very beginning, we define
the stochastic integral M_T=int_0^T V_t dW_t for the processes V which are
square integrable: E(int_0^T V^2 dt)<\infty. And then it can be shown that
the process (M_t)_{0<=t<=T} is a square integrable martingale. This is just
your case since E(int_0^T |W_t|^2 dt)=int_0^T E(W_t)^2 dt=T^2/2<\infty.
be
【在 x********o 的大作中提到】
: the interviewer told me that int_0^T |W_t|dW_t is not a martingale.
: I am really confused. by the martingale representation theorem, it should be
: a martingale.
: where is wrong?
: Thanks for any explanation in advance.
|
|
|
l*******1
发帖数: 113 | 21 write |w| as sqrt(w^2)
so w^2 = (sqrt(w^2))^2
so d(w^2)/dw = 2(sqrt(w^2))=2|w|
d|w|/dw= 2w/|w|
use ito on (|w|)^2
we can get
int_0^T |W_t|dW_t = 0.5* W^2 - 0.5 * int_0^T (W_t / |W_t|) dt
note in the case of
int_0^T W_t dW_t = 0.5* W^2 - 0.5 * t (expectation 0)
since W_t / |W_t| <= W_t / W_t = 1
E(int_0^T |W_t|dW_t ) > 0
so this is not a martingale |
e**********n
发帖数: 359 | 22 Not even wrong.
【在 l*******1 的大作中提到】
: write |w| as sqrt(w^2)
: so w^2 = (sqrt(w^2))^2
: so d(w^2)/dw = 2(sqrt(w^2))=2|w|
: d|w|/dw= 2w/|w|
: use ito on (|w|)^2
: we can get
: int_0^T |W_t|dW_t = 0.5* W^2 - 0.5 * int_0^T (W_t / |W_t|) dt
: note in the case of
: int_0^T W_t dW_t = 0.5* W^2 - 0.5 * t (expectation 0)
: since W_t / |W_t| <= W_t / W_t = 1
|
t*******e
发帖数: 172 | 23 joke?
do you really know what you are talking about? Please offer me a definition
of square integral martingale....
distribution as W(t)/W(t)>0.
【在 l****o 的大作中提到】
: check the property of a special form of girsanov's SDE's solution.
|
x********o
发帖数: 519 | 24 Hey, laonuo,
we are all waiting for you to give your solution.
【在 l****o 的大作中提到】
: 这种题目都不会，回家好好看两个月书，再出来投简历。不是贬低你，没准备好就乱投
: 简历，很多好机会就浪费了。
|
l****o
发帖数: 2909 | 25 First of all, |W(t)| is F(t)-measurable, where F(t) is generated by W(t).
Secondly, E[\int_0^T|W_t|^2 dt] =\int_0^T E[|W_t|^2] dt=\int_0^T t dt=T^2/2
<\infty. This proves that it sufficiently satisfy ITO itegration
definition. Therefore it is a martingale. Here you can use standard machine and
L^P space definition for more rigorous proof on how to construct a general integrand from simple integrand.
Thirdly, E[[\int_0^T|W_t| dw(t)]^2]=E[\int_0^T|W_t|^2 dt] =\int_0^T E[|W_t|^
2] dt=\int_0^T t dt=T^2/2 <\infty. This proves that it is a square
integrable martingale.
Fourthly, to generalize, if E\int_0^T[a(t)]^s dt <\infty, then M(t), 0
is a square integral martingale. If \int_0^T[a(t)]^s dt <\infty, P a.s.,
then M(t), 0
【在 x********o 的大作中提到】
: Hey, laonuo,
: we are all waiting for you to give your solution.
|
x********o
发帖数: 519 | 26 didn't you say it is not a martingale?
thought you would give us a surprise.
2
machine and
integrand from simple integrand.
|^
T
【在 l****o 的大作中提到】
: First of all, |W(t)| is F(t)-measurable, where F(t) is generated by W(t).
: Secondly, E[\int_0^T|W_t|^2 dt] =\int_0^T E[|W_t|^2] dt=\int_0^T t dt=T^2/2
: <\infty. This proves that it sufficiently satisfy ITO itegration
: definition. Therefore it is a martingale. Here you can use standard machine and
: L^P space definition for more rigorous proof on how to construct a general integrand from simple integrand.
: Thirdly, E[[\int_0^T|W_t| dw(t)]^2]=E[\int_0^T|W_t|^2 dt] =\int_0^T E[|W_t|^
: 2] dt=\int_0^T t dt=T^2/2 <\infty. This proves that it is a square
: integrable martingale.
: Fourthly, to generalize, if E\int_0^T[a(t)]^s dt <\infty, then M(t), 0: is a square integral martingale. If \int_0^T[a(t)]^s dt <\infty, P a.s.,
|
l****o
发帖数: 2909 | 27 if you speak out what I just wrte, I doubt that the interviewer will say you
are wrong. That is why I said that you should go back to review books and
then start to send your CV. You obviously failed to convince that you are
solid enough to let people believe you are right.
【在 x********o 的大作中提到】
: didn't you say it is not a martingale?
: thought you would give us a surprise.
:
: 2
: machine and
: integrand from simple integrand.
: |^
: T
|
x****e
发帖数: 1780 | 28 sha bi
the
gave
for
【在 l*****y 的大作中提到】
: If they reject you only because you couldn't figure out the problems, just
: let it be. I'm pretty sure you would have a hard time getting adapted to the
: atmosphere even if you were hired.
: A lot of ppl were asking how to solve xxx after the interviews. Someone gave
: you the answer, probably after a 1/2/5/10/30 min consideration. So what?
: You are expecting the same questions or the ones you were fully prepared for
: in the next interview? From my experience, that really has a low
: probability. And if you couldn't figure out a single question within the
: first minute, you have already left an impression to the interviewer that
: you are not solid on that part. And based on the various background of the
|
m******g
发帖数: 12 | 29 This is a freaking bloody fuking stupid martingale. |
r*******y
发帖数: 1081 | 30 if it is defined by ito integral, then it is a martingale,
but if it is defined by stratonovich integral, then it is not a martingale
be
【在 x********o 的大作中提到】
: the interviewer told me that int_0^T |W_t|dW_t is not a martingale.
: I am really confused. by the martingale representation theorem, it should be
: a martingale.
: where is wrong?
: Thanks for any explanation in advance.
|
