Stratonovich integral is somehow easier to understand, because it's more like the simple Lebesgue integral. For example, d(B^2)=2BdB for Stratonovich, but not for Ito.It's of little use in finance though, due to already mentioned "forward looking" properties.

<t>QuoteOriginally posted by: AntoniosI have just read the argument of Artzner et al. on the coherence of VaR. Along that I have gone through the papers of Acerbi-Tasche and the work of Rockafellar/Uryasev. What it is not clear to be is an issue towards the alternative coherent measures suggested in...

<t>QuoteOriginally posted by: crowlogicHow exactly do you plan to draw numbers independently? It is impossible to generate random numbers. As such, the problem doesn't even make sense so how do you plan to solve it?That's some kind of epidemia, isn't it? First, N starts to question the existence of ...

<t>QuoteOriginally posted by: gardener3So what's the answer to amiraliev's question? It seems a proper distribution would have to taper off at one or both tails, but I don't see how you could use this info to get better then 50% accuracy.Well, mhughes gave the right answer several posts before. I wr...

<t>QuoteOriginally posted by: NQuoteOriginally posted by: amiralievListen N, what point do you want to make? Don't you think the statements likeQuotePlease, give me some reasons why I shouldn't think that those who teach stochastic calculus are total idiots...(or indeed like "there is no such thing ...

Listen N, what point do you want to make? Don't you think the statements likeQuotePlease, give me some reasons why I shouldn't think that those who teach stochastic calculus are total idiots...(or indeed like "there is no such thing as random") are a little bit strange?

QuoteOriginally posted by: crowlogicI agree there is no uniform distribution "on the reals", ...Very good. As always, there was nothing to argue about.

<r>QuoteOriginally posted by: crowlogicits simple non-increasing ramp functionf(x)=0 : x<=0f(x)=x : 0<x<1f(x)=1 <E>:x</E>>=1hence f(-inf)=f(0)=0 and f(+inf)=f(1)=1 You change your point of view so rapidly I'm a little bit confused . So, am I right to understand your position: that this uniform on [0...

QuoteOriginally posted by: crowlogicTake the derivatives of each of those functions, square it, the integral from 0 to 1 = 1That doesn't make it a distribution function.

<t>QuoteOriginally posted by: crowlogicWhat you said is not entirely correct. There exists countable infinite sets of distributions over the interval [0,1] all with the same probability measure 0 (Lebesgue null measure). The union of null sets is also null which is obviously not infinite, because po...

[quote]Having an infinite measure is not a contradiction, its an oppurtunity to explore differerent concepts of measure and convergence.[/quote]Don't be stupid, we were talking about probability measure that player uses to generate r.v. .

I think CAPM, BS or even mean-variance should be viewed as a concepts, not as the "theories of everything". It's just the framework you can use when looking on things. In this sense the concept couldn't be "right" or "wrong".

Mathematically, EMH is that market is a martingale. I have not seen a paper yet that would devise a criterion to test it (in the statistics terms), but it's not impossible. By the way, martingales could be non-Markovian easily (and most of them are).

MrMartingale, I don't say anything about tricks. You don't have to know a trick to compute 123*234 - you have an algorithm. You don't have to know a trick to open the brackets and take the expectation. You also don't have to know anything about statistics to take expectations.

<t>>> Trust me that the fact that dividing by n-1 gives an unbiased estimator is not a fact that would normally be called "obvious" in mathematical discourse.Well, as the math student, I can reassure you that most of my fellow students would call this fact obvious. >> Most people would not be able t...