determine if something is martingale

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niceseb
Posts: 7
Joined: Thu Nov 03, 2011 8:25 pm

determine if something is martingale

Postby niceseb » Tue Mar 06, 2012 12:13 am

Do I approach the following 3 examples in the same way to determine whether they are martingale or not?

1. Y(t) = X(t) + 4t

2. Y(t) = t^2 X(t) - 2 Integrate(from 0 to t) [s X(s) ds]

3. Y(t) = X1(t) X2(t)

Where X(t), X1(t) X2(t) are standard Brownian motions
and X1(t) X2(t) correlation rho so that dX1(t) dX2(t) -> rho dt. Does the answer depend on the value of rho?



Sebastian

niceseb
Posts: 7
Joined: Thu Nov 03, 2011 8:25 pm

Re: determine if something is martingale

Postby niceseb » Tue Mar 06, 2012 12:32 am

Worked out 2. to be all zeros?

niceseb
Posts: 7
Joined: Thu Nov 03, 2011 8:25 pm

Re: determine if something is martingale

Postby niceseb » Tue Mar 06, 2012 1:23 pm

1. Is not Martingale, since dt coefficients not zero.

coalexander
Posts: 815
Joined: Sun Sep 28, 2008 10:30 pm

Re: determine if something is martingale

Postby coalexander » Thu Mar 08, 2012 2:51 pm

Dear Sebastian

I think you may have misunderstood the purpose of this forum, which is to ask questions or make comments that are directly relevant to the text of each book. This question and your two questions appear more like problems that might be set from a university course.

Carol


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