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Old 07-07-2014, 09:42 AM
Hawthornen Hawthornen is offline
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Default Ito Lemma question

So I've been struggling with a somewhat fundamental part of Ito's lemma and maybe someone could help explain what's going on.

In one of my sample problems (changed slightly)

dS(t)/S(t) = .3dt + .4dZ(t)
G(t) = S(t)^t

And it wants me to basically find a stochastic differential equations satisfied by G(t)


When I attempt to work out the partial derivatives I feel like the variables I differentiate with regard to are opposite to that in the solution.

For example: the partial derivative with regard to S(t) is listed as t*S(t)^(t-1)
and the partial with regard to t is ln(S)*S^t

To me this always seems backwards. Maybe I'm missing something or just looking at it wrong but my first partial derivatives are correct but for the wrong variables (so my second partial is always incorrect). Maybe someone could explain where I'm going wrong.
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Old 07-07-2014, 09:57 AM
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kernel kernel is offline
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Ask yourself what the derivative of the following would be from a calculus one class:

1. y = x^5

2. y = 5^x
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Old 07-07-2014, 11:39 AM
mono/poly mono/poly is offline
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Partial derivative with respect to S --> treat S as a variable, t as a numerical constant
Partial derivative with respect to t --> treat t as a variable, S as a numerical constant
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Old 07-07-2014, 12:27 PM
Hawthornen Hawthornen is offline
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Holy crud thanks guys. I've done plenty of partials. I must be just tired or something, I don't know why I was getting that so backwards.

Appreciate the help.
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Last edited by Hawthornen; 07-08-2014 at 08:12 AM..
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