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CrashedMint
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November 11th, 2008, 9:53 pm

What is the solution? I don't get it. :-(
 
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ppauper
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November 12th, 2008, 1:22 pm

w(T)-w(0) ?
 
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list
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November 12th, 2008, 3:48 pm

it is a normal r.v. having m=0 the second moment could be calculated if you take into account that Ew(t) w(s) = min(s,t)
 
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Alan
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November 12th, 2008, 4:29 pm

Yes, list is correct.This is a FAQ that never was ... ahem
 
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ppauper
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November 12th, 2008, 7:06 pm

so w_t doesn't mean (dw/dt) here ?
 
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Alan
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November 12th, 2008, 7:23 pm

No, the OP will amost certainly say it means W(t), a Brownian motion.
 
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Cuchulainn
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November 12th, 2008, 7:23 pm

dbl
Last edited by Cuchulainn on November 11th, 2008, 11:00 pm, edited 1 time in total.
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Cuchulainn
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November 12th, 2008, 7:26 pm

QuoteOriginally posted by: ppauperso w_t doesn't mean (dw/dt) here ?When I first say SDEs I thought the same. It is very confusing indeed. They mean w(t). I went to a training once and it was into day 2 that I realised what it was (trainer assumed everyone's background was the same).I reckon X% of writers use the first notation and (100-X)% use the other notation.
Last edited by Cuchulainn on November 11th, 2008, 11:00 pm, edited 1 time in total.
Step over the gap, not into it. Watch the space between platform and train.
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CrashedMint
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November 12th, 2008, 10:23 pm

Umm, actually i meant to ask for the integral of a standard wiener process with respect to time. I found this as a question in Crack's book, but his answer is like 2 pages long. Can that be? should this be something very simple with a very simple solution like w(T)?
 
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list
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November 12th, 2008, 10:52 pm

integrate by parts and you get T W(T) - int from 0 to T " tdw(t)" if tis you like it better.
 
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CrashedMint
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November 12th, 2008, 11:08 pm

like this?
 
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mj
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November 13th, 2008, 1:25 am

it's a linear combination of normals with mean zero so it's a normal with mean zero. You just have to compute the variance. One easy way to do it is just to approximate by a sum of N pieces and let N go to infinity.The answer is not W_T.
Last edited by mj on November 12th, 2008, 11:00 pm, edited 1 time in total.
 
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phil451
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November 21st, 2008, 7:57 am

This is a Stochastic Integral which cannot be solved by standard deterministic methods. If you want to get serious about financial engineering then you really need to learn how this works. Unfortunately, there is no easy solution and you really have to thinkThe approach to solving it is similar to solving a deterministic integral using Rienmann sums. So, you have to understand the concept of summing with letting n tend to infinity.The chapter on Stochastic Integration in Paul Wilmott's Introduction to Quantitative Finance will help to get you started with Brownian Motion, particularly the coin tossing example and then i would suggest 'Kwok' which has just been re-issued.Good Luck!
 
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Jeriot
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November 22nd, 2008, 6:40 am

Thanks mint, that made me feel a lot better. I don't get it either. Didn't get it when I took that module, still don't get it now.If I do it as the gurus suggested, thenAlas, that's the limit of my understanding. I presume since we do not have knowledge of w_t values past t=0, we would not be able to come up with a value for the integral but we know the expected value would be zero.I'd like to know what the solution is tho, if you could scan that 2 page answer or something. Don't wanna remain ditzy all my life
 
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mj
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November 23rd, 2008, 5:39 am

it's a sum of normals so it's normal. We know it's mean so all we need is the variance. This is not hard to compute if we first compute the covariance of w_i and w_j for i \neq j.
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