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Anonymous
A proof of Ito's formula ? 2017-03-24 11:29:37 Post No. 8775287
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A proof of Ito's formula ? 2017-03-24 11:29:37 Post No. 8775287
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Does /sci/ has a link to the proof of the Itô formula ? If [math]f \in \mathcal{C}^1 (\mathbb{R_+}) \times \mathcal{C}^2( \mathbb{R})[/math] and
[math]X_t = X_0 + \int_0^t K_s ds + \int_0^t H_s dWs[/math]
then :
[eqn]f(t,X_t) = f(0,X_0) + \int_0^t \frac{ \partial f}{ \partial t}(s,X_s) ds + \int_0^t \frac{\partial f}{\partial x}(s,X_s) dX_s \\
+ \frac12\int_0^t\frac{\partial^2 f}{\partial x^2}(s,X_s) d\langle X,X \rangle_s [/eqn]
Where
[eqn] \langle X,X \rangle_t = \int_0^t H_s^2 ds[/eqn] so that
[eqn]d \langle X,X \rangle_s = H_s^2 ds[/eqn]
I made some research on the net but did not found any proof, only "elements of proof".
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>>8775287
I got one in the book 'Financial Calculus' by Alison Etheridge.
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>>8775287
Good question actually. I remember searching for this some time ago, and the only things I found were watered down proofs for finance/econometrics majors.
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>>8776320
Did some professor made a proof in his online course, in at least one american university ?
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>>8775287
can you read french?
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>>8777138
Yes.
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>>8777153
This pdf should be useful
https://www.google.fr/url?sa=t&rct=j&q=&esrc=s&source=web&cd=7&ved=0ahUKEwiW0qCvgPLSAhWKuhoKHXp8A9oQFghEMAY&url=https%3A%2F%2Fwww.math.ens.fr%2Fenseignement%2Ftelecharger_fichier.php%3Ffichier%3D525&usg=AFQjCNFcMBcVkBYC6S886SzvNtfjtVwzfw&sig2=iKkgPSWbcsYxTQ7eRAwEVQ
google "Equations différentielles stochastiques en dimension finie et infinie bouafia benezech"
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>>8777153
>can you read french?
>yes
patrician af. I'm considering learning French just so I can read French math texts.
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>>8775287
>stats
>proofs for formula
all stats is based on non-rigorous guessing work at best.
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>>8777265
didn't mean it that way, but the french like to prove every single thing, even if it looks tedious. I don't know russian or german so it's my best bet for reading good mathematics.
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>>8777323
it's stochastic calculus, not stats, you inbred brainlet
stochastic calculus leads to SDEs which are inherently connected to PDEs, so basically it's god tier math
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I have no idea what this formula is about or what the variables mean, but it looks like a simple application of multivariable Taylor series to f
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>>8777335
>*DEs
>god tier
LOL, so this is the power of an applied math brainlet.
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>>8777339
have fun starving to death
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>>8777339
this
I had a course on PDE theory and it was awfully boring, why anyone would decide to study full time is beyond me
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>>8777138
any french course on finance has it, wtf
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>>8777353
brainlets who move to finance
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>>8777184
>https://www.google.fr/url?sa=t&rct=j&q=&esrc=s&source=web&cd=7&ved=0ahUKEwiW0qCvgPLSAhWKuhoKHXp8A9oQFghEMAY&url=https%3A%2F%2Fwww.math.ens.fr%2Fenseignement%2Ftelecharger_fichier.php%3Ffichier%3D525&usg=AFQjCNFcMBcVkBYC6S886SzvNtfjtVwzfw&sig2=iKkgPSWbcsYxTQ7eRAwEVQ
Bretty good desu :DDDD
Thanks.
>>8777434
No because infinance degrees, there are some people from business schools. They can not handle complicated proof.
>>8777438
Both finance and optimization.
Yes, applied maths.
Yes I want to have a confortable life and learn (((pure maths))) by myself when I will have time.
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