The market is a controlled dynamic system. - page 342

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Fast528:
don't see any discussion, does anyone even understand what the ***341 page is? It's been 7 years.

Read thoughtfully. It's about how to manage the market dynamically on a systematic basis.

 
Nothing in the real world is perfect. This is also true of randomness. For example, when we need random numbers, we have to make do with pseudorandom numbers (PRNG). Any such generator is a dynamic system. Here is an example - below is the code on R and two charts drawn by it, which differ only in the value of p - the probability of moving up one step, in the first case p=0.5 and p=0.6 in the second. Knowing this code, we can absolutely precisely predict how these curves will look for any given n - number of steps.
seed <- 10
set.seed(seed)
n <- 100; p <- 0.5; q <- 1.0 - p
s <- sample(c(1,-1), n, r=TRUE, p=c(p,q))
cs <- cumsum(c(100, s))
plot(cs, t="l")
p = 0.5
p = 0.6
Imagine now that we know all this code apart from the first line (initialization of the MF generator), and we also have the initial part of the graph. Would we be able to accurately reconstruct the rest of the graph? Unlikely. We would have to go through a long search for that unknown number and we may make a mistake - with different values of the initializer the initial parts of the graph may be the same and the subsequent parts may be different. This is a simple example of what is called dynamic chaos - any small inaccuracy leads to impossibility of prediction, despite the absolute determinism.

Therefore, one has to use the methods of probability theory. From such an incomplete code or even just from a graph it is easy to conclude, for example, that the trend is much more pronounced in the second picture.

It is also worth recalling the Takens theorem due to which the notion of dimensionality of lag space embedding is defined for a dynamic system. The greater this dimensionality, the closer the system is to random. For the Lorenz system and in your examples it is quite small (less than 10), for a good PRNG it is at least 100, for the market (if I understand Peters correctly) it is at least 1000.
 

This is an entirely different task... not having a practical orientation.

And I am familiar with TViMS, and so much so that I have developed stochastic boosters. (if that means anything to you).

Look in the direction of tracking systems. Literature is available.

 
Олег avtomat:

This is an entirely different task... not having a practical orientation.

And I am familiar with TViMS, and so much so that I have developed stochastic boosters. (if that means anything to you).

Look in the direction of tracking systems. Literature is available.

I wasn't trying to build a practical theory. I simply gave an example of how knowing that something is a dynamic system can be useless. I also showed that if the market is a dynamic system, it is a highly complex one.

As for useful theory, it seems to me that it should be built on game theory and not just optimization (like the fields you mentioned). Perhaps this would allow at least some consideration of the impact of market makers on the market.

 
Aleksey Nikolayev:

I wasn't trying to build a practical theory. I simply gave an example of how the knowledge that something is a dynamic system can be useless. I also showed that if the market is a dynamic system, it's a very complex one.

As for useful theory, it seems to me that it should be built on game theory and not just optimization (like the fields you mentioned). Perhaps this would allow at least some consideration of the impact of market makers on the market.

"I wasn't trying to build a practical theory" --- and in vain...

"knowing that something is a dynamic system can be unhelpful" --- this is the case when considering a static problem. (which yours was)

"if the market is a dynamic system, it's a very complex one" --- that's right, it is.

"it should be based on game theory" --- that's a very promising area for further research.

"not just optimisation" --- firstly, this combination of the words "just optimisation" indicates a lack of understanding of what it is; secondly, optimisation is never easy if only because of the choice of an acceptable optimisation criterion that takes into account existing contradictions, and other related inconsistencies, both at the justification and implementation level.


Let me remind you of the meaning of the term 'optimality': the property of being the best in some respect.

 
Олег avtomat:

It's not that I think optimisation is anything simple. It is about the fact that in game theory it looks like a very degenerate case - a one-man game. Here is an excerpt from the book.

intro

I also find this theory very promising. I found very interesting the statement of Keynes, who was not only an economist, but also a successful trader:

Keynes compared a professional investor to a contestant in a newspaper who has to choose the six most attractive faces out of 100 pictures, and the one who is closest to the average reader's preference wins: "This is not the case when we choose the most attractive faces for us, and not even when we choose the faces most attractive according to the average reader's opinion. We have reached the third stage, where we apply our mental faculties to predict what the average opinion would be. And, I believe, there are some who practice the fourth, fifth and higher levels."

 
Aleksey Nikolayev:

It's not that I think optimisation is anything simple. It's about the fact that, within game theory, it looks like a very degenerate case - a one-man game.

Not really. In this case, the second party (seen as a single player, or as a coalition) is the external environment, whose opposition is indirectly expressed through control error.

In terms of game theory, however, it is necessary to identify the strategy of the opposing party
du = Au + Bv
dv = Cu + Dv
It is possible to make such an estimate. But it has to be done, again, through the control error (incoherence).

Have you taken any steps in this direction yet?

 
Олег avtomat:

Not quite so. In this case, the second party (seen as an individual player or as a coalition) is the external environment, whose opposition is indirectly expressed through management error.

In the framework of game theory, it is necessary to identify the strategy of the opposite side
du = Au + Bv
dv = Cu + Dv
It is possible to make such an estimate. But it has to be done, again, through the control error (incoherence).

Have you taken any steps in this direction yet?

This is true in the case of what is called "playing with nature". In the case of playing with man, anticipating the opponent's strategy will result in him changing it, taking that anticipation into account. This is roughly what Keynes talks about.

I am not very strong in this science - I always perceived it as meaningless fiddling with matrices. Now I realise that I was wrong and am trying to catch up - I am studying the literature and trying to build simple models. I haven't got any results yet, but I came to a conclusion that perhaps the theory of stochastic games would be useful.

 
Aleksey Nikolayev:

This is true in the case of what is called "playing with nature". In the case of a game with humans, anticipating the opponent's strategy will cause him to change it, taking that anticipation into account. This is roughly what Keynes talks about.

I am not very strong in this science - I always perceived it as meaningless fiddling with matrices. Now I realise that I was wrong and am trying to catch up - I am studying the literature and trying to build simple models. So far I haven't received any results, but I came to a conclusion that perhaps the theory of stochastic games would be useful.

Trading by chart of an instrument is more like "playing with nature" or "playing with the market elements". In this case it is not a "game with a man", who purposefully changes his game by reflecting on the play of a small element of a huge market element. This effect is possible in the case of trading of huge volumes (central banks, hedge funds), but it is impossible for the petty trader who is unable to influence the dynamics of an instrument with his actions.

If the theory is based on the Markov process, i.e. ignoring all of the previous dynamics, then such a theory can only be local. It cannot take into account the dynamics of the process development on a long time interval.
 
Олег avtomat:

Trading a trader by the chart of an instrument is more like "playing with nature" or "playing with the market elements". In this case we are not talking about "playing with man", who purposefully changes his game by reflecting on the play of a small element of a huge market element. Such an effect is possible in the case of trading with large volumes (central banks, hedge funds), but it is impossible for a single small trader who cannot influence the dynamics of an instrument with his actions.

If the theory is based on a Markovian process, i.e. ignoring all the previous dynamics, such a theory can only be local. It is not able to take into account the dynamics of the process over a long period of time.

No, the players are not individual traders, but some homogeneous groups of traders, into which the totality of them is divided. The same is true for institutional market participants - they are divided into one or more homogeneous groups, each of which is considered a separate player.

The target is of course much more modest than the impact on price. I would like to use simple examples to understand the possible mechanism leading to its non-stationarity.

The system as a whole may be Markovian, but the price series itself may well be non-Markovian.

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