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i am really enjoying your presence here at ET martingale, but your sig is doing a good job of mystifying me. care to illuminate?

'The history of public debt is full of irony. It rarely follows our ideas of order and justice.' Thomas Piketty
by melo (melometa4(at)gmail.com) on Sun Aug 17th, 2008 at 01:53:03 AM EST
[ Parent ]
I believe it's a definition of martingale, taken from TeX file.
by Sargon on Sun Aug 17th, 2008 at 03:33:46 AM EST
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I've had that sig on other scoop sites, before they had picture embedding macros, and I've kept it for sentimental reasons :)

It's a piece of LaTeX which represents the defining property of a martingale.

The simplest example of a martingale in this sense is a double or nothing gambling strategy in certain games of chance(*), but a better way of understanding them is that they are purely random processes, which cannot be predicted based on historical observations: if you try to predict their future, your best guess is to duplicate the present, regardless of what you've seen in the past.

(*)wherein one proves that double or nothing fails to help one win: when the strategy has no statistical trend, then there is no advantage from using it.

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$E(X_t|F_s) = X_s,\quad t > s$

by martingale on Sun Aug 17th, 2008 at 03:44:38 AM EST
[ Parent ]
um, thanks, clear as day

'The history of public debt is full of irony. It rarely follows our ideas of order and justice.' Thomas Piketty
by melo (melometa4(at)gmail.com) on Sun Aug 17th, 2008 at 05:06:29 AM EST
[ Parent ]
Thanks.  You learn something new every day.  Presumably the political analogy is that you should escalate a conflict unless you have the means to win at the escalated level - something Putin seems to understand rather well.

It's time I got out of this game....
by Frank Schnittger (mail Frankschnittger at hot male dotty communists) on Sun Aug 17th, 2008 at 07:19:30 AM EST
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Of course, international games of diplomacy are a lot more difficult to analyze than simple gambles with well defined rules. Yet the neocons do seem to behave like addicted gamblers on a losing streak of late, don't they?

--
$E(X_t|F_s) = X_s,\quad t > s$
by martingale on Sun Aug 17th, 2008 at 08:15:59 PM EST
[ Parent ]
You read French, and you are interested in game theory - you just HAVE to read my PhD dissertation on the independence of Ukraine (long title: "the independence of a country: what game theory can tell us and the exemple of Ukraine"

In the long run, we're all dead. John Maynard Keynes
by Jerome a Paris (etg@eurotrib.com) on Mon Aug 18th, 2008 at 06:09:48 AM EST
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Did you even publish a journal paper based on the thesis?
by Sargon on Mon Aug 18th, 2008 at 06:54:23 AM EST
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Sadly, no. My jury professors disagreed between themselves, and the one that ran publications was not happy that I had, according to him, pledged allegiance to a rival school of thought, and he thus vetoed any publication.

As I was not staying in academia, I did not really care and did not fight this. Thus the dissertation was never published anywhere and was quickly forgotten.

I had done an executive summary in English but can no longer find the file; I'd need to draft it again; it's probably worth it...

In the long run, we're all dead. John Maynard Keynes

by Jerome a Paris (etg@eurotrib.com) on Mon Aug 18th, 2008 at 07:12:38 AM EST
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Sounds very interesting. Do you have the document on the web or someplace I can download it?

Sinon, tu peux aussi m'envoyer le fichier par email, l'addresse que j'ai indiquee sur ET lors de l'enregistrement est bidon, mais fonctionne.

--
$E(X_t|F_s) = X_s,\quad t > s$

by martingale on Mon Aug 18th, 2008 at 09:30:20 PM EST
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