The market is a controlled dynamic system. - page 381
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The articles were cited as further evidence of the well-known fact that excessive risk can make a profitable strategy unprofitable.
The articles use a quite common model of trading results as a sequence of trades with independent equally distributed returns. The market model as such is not constructed - the only standard reasoning is given as to why trades can be considered as such (in a certain approximation).
I am not refuting the statement that it is impossible to earn on SB. I formalize it mathematically, so that those who wish can check it for themselves, using the theory of Ito's stochastic calculus.
1) Of course, it is absolutely true that excessive risk can make a profitable strategy unprofitable.
2) It is not surprising that if you "use a quite common model of trade results as a sequence of trades with independent equally distributed returns", your results are virtually no different in any significant way from those of "quite common models". And that's correct. That's the way it should be.
3) Please remind me of your formalization of the impossibility of making money on SB. And those who wish can check it for themselves. And it is not necessary to useIto's stochastic calculus theory, although to complete the picture, this method can be included into the arsenal of research methods of your formalization of "impossibility to earn money on SB". There are other research methods, much more powerful. For example, the same integral of Ito can be represented as a dynamic process, and this gives very powerful research tools, which you do not have.
My theory is quite simple. In it, risk is a regular sample value (like the mean, for example). But its construction is more complex (than the mean) and you have to resort to Monte Carlo simulation to get its distribution function. To select a particular value of risk, you must set the level of significance and take the quantile corresponding to it. Thus 1.5% is the value corresponding to a certain level of significance. This level can be increased and a larger value for the risk can be obtained, but it will lead to an increase of probability that the system will give a small profit and/or large drawdown, while remaining potentially profitable - this is approximately whatMaxim Kuznetsov wrote above.
1) In the behavior of markets, their uncertainty in the future is evident. The most common way to mathematically model this uncertainty - the probability theory. In this framework, prices are considered as a random process.
2) If prices are a random process, then the trader's capital is always a random process. Deterministic transformation of a random process is also a random process. Theoretically, this process can sometimes degenerate into a deterministic function. For example, at zero position it represents a constant)
3) With symmetric SB for any TS the capital will be a martingale - a process with constant mathematical expectation equal to the initial capital. This means that for any TS there will always be both profitable and loss-making realization of SB, and on the average there will always be zero capital gain (negative when the spread is taken into account). How this happens can easily be seen even with a "buy and hold" strategy.
The main thing in the approaches to the market is profit, and it happens with a rather strange approach.)
What is your theory?
1. No
2. A theory should not make assumptions
3. The word 'always' still needs to be proved.
And in general, any theory is built on evidence.
3) Please remind me of this formalisation of your inability to make money from SB. And those who wish can check it for themselves. And it is not necessary to use the theoryof stochastic calculus Ito for this purpose, although to complete the picture, this method can be included into the arsenal of methods of research of your formalization "impossibility to earn money on SB". There are other methods of research, much more powerful. For example, the same integral of Ito can be represented as a dynamic process, and this gives very powerful research tools that you do not have.
The capital of any TS on a symmetrical SB is a martingale.
To introduce the notion of an integral, ito needs to introduce the notion of a Wiener process. Is it a dynamical system too?
The capital of any TS on a symmetric SB is a martingale.
To introduce the notion of an integral Ito needs to introduce the notion of a Wiener process. Is it a dynamical system too?
1) Express it in a formalized form. Please.
2) Sure. If you don't know how, I'll give you a hint.
Your theory?
1. No
2. There should be no assumptions in the theory
3. The word "always" has yet to be proven.
And in general, any theory is built on proofs.
Mine, in the sense of what I have written in my articles (not invented by me, of course). Although, the articles are not mine either)
1) For traders the uncertainty is obvious. Just read this forum.
2) Any theory is built on the basis of certain assumptions (usually called definitions, axioms, postulates, etc.)
3)The capital of any TS on a symmetric SB is a martingale (expectation is a constant).
1) Express this in a formalised way. Please.
2) Sure. If you don't know how, I'll give you a hint.
1) Capital is equal to Integral Ito of the position volume of a Wiener process. The position volume is a piecewise constant process with discontinuity points at Markovian points in time. As a result, we obtain a martingale.
2) Any random process is, by definition, a family of random variables. Is a random variable also defined through dynamical systems?
The question that needs to be asked is what in forex (specifically here) can be called a random process and to what extent.
Without defining this, without separating flies from kittens, all reasoning and calculations are "floating".
To clarify: there are physical constraints on any range of time (or limit to fluctuations). They come from monetarypolicy, currency regulations and laws/acts/statutes/rules of the participants, the agreed currency basket.
And the whole trading process is "random" only to a certain extent, inside a permissible window. After all, currencies are not only "objects of speculation" but they are also a means of payment in the main, they also have purchasing power. :-)
1) Capital is equal to Integral Ito of the position volume of a Wiener process. The position volume is a piecewise constant process with breakpoints at Markovian points in time. As a result, we obtain a martingale.
2) Any random process is, by definition, a family of random variables. Is a random variable also defined by you through dynamical systems?
1) These are your words:"I am not refuting the claim that it is impossible to make money on SB. I formalize it mathematically" Where is this mathematical formalization? I am not asking for a verbal description of your understanding of all this nonsense, buta mathematical formalization of it.
2) Apparently you are not familiar with the concept of a shaping filter.
1) These are your words:"I am not refuting the claim that it is impossible to make money on SB. Where is this mathematical formalization? I am not asking for a verbal description of your understanding of the whole thing, buta mathematical formalization of it.
2) Apparently you are not familiar with the concept of a shaping filter.
1) Demonstrate an understanding of what a martingale is, then I'll write more.
2) More likely you are unfamiliar with the basics of probability theory.
The question that needs to be asked is what in forex (specifically here) can be called a random process and to what extent.
Without defining this, without separating the flies from the chaff, all reasoning and conclusions are "floating".
To clarify: there are physical constraints on any range of time (or fluctuation limit). They come from monetarypolicy, currency regulations and the laws/acts/statutes/rules of the participants, the agreed basket of currencies.
And the whole trading process is "random" only to a certain extent, inside a permissible window. After all, currencies are not only "objects of speculation" but they are also a means of payment in the main, they also have purchasing power. :-)
There is a joke: "nothing is random in random processes")
There is a sense to use them only if there are some regularities in randomness - like presence of event frequencies convergence. Sometimes such regularities are not detectable (due to paucity of data, for example) then they are just postulated).
The problem is that there are no other approaches for modelling uncertainty that are as developed.