The only possible answer is no. You've already read some fundamental reason for it: different targets, human behavior, inhomogeneity. In addition we have, and that is crucial here, very diverging levels of information, and by the way as well costs. Furthermore, there will be natural and political disturbances which are impossible to predict. You will have to make so many assumptions to derive a model, that the result will be exactly this: a model under idealized conditions. Add yours to the hundreds we already have.
Q-1 said:
What does that mean? Until the law of large numbers takes place? Considering the modern trade mechanisms, aren't we already there? Anyway, how much time is time?
... wouldn't market behaviour converge ...
It already does. It's called daily fixing.
... on what is most rational...
Undefined. Assumption.
... if irrational behaviour ...
Again undefined.
... could be foreseen based on knowledge ...
Assumption, that such a knowledge can be achieved.
... of market psychology?
No. And if all the above didn't convince you, here are two further objections:
- Supermarkets already work this way. Nevertheless, they cannot precisely predict consumers behavior, for otherwise they wouldn't waste so much goods and thus money day by day.
- The pure number of variables, initial conditions, prize building relevant events are way beyond any current possibility to handle.
I'm under the impression...
Opinion.
... that speculative and such types of volatility trading would recede towards trading based on fundamentals...
That's what economists dream of. In reality, this is another, and in my experience, completely wrong assumption. To buy 500,000 IBM on Monday and sell them on Thursday has absolutely nothing to do with fundamentals. But despite of this, it's analysts' daily bread and happens all the time in countless offices.
... and arbitrage trading.
Again an assumption. Arbitrage trading takes place, but rarely leads to an equilibrium as theories assume. Have a look on such a simple thing as currencies and compare the Euro prize in Chicago with the Dollar prize in Frankfurt on single days. Not to mention the time lag!