Matstat Econometrics Matan - page 35
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Market time is discrete because the market flow of events - bids, deals - is discrete.
Bids and trades do not occur at fixed points in time. Usually Poisson flow models are used for such phenomena. Time in them is continuous.
I believe willingly, but why is it necessary? It makes no sense to interpolate something between two ticks, because what happens between ticks is determined by a more detailed discrete stream of events at Level2 and Level3.
Some analogy could be a science like hydrodynamics (or all continuum mechanics in general), where the atomicity of real matter is usually not taken into account.
This simplifies (makes possible in principle) many calculations.
More specifically, one can understand it by reading, for example, about modern portfolio theory or theory related to options.
However, it is highly desirable that the equity would still be consistent with this model. At a minimum, this is needed to make a portfolio of systems.
This leads to auxiliary metrics that in some sense measure the fit of the equity to this model. For example, this is the significance level that the drift is positive and/or the significance level that there is no correlation between the increments.
When constructing a portfolio of systems, new metrics emerge - the correlation matrix and the (auxiliary) significance level of those correlations.
In my view, it is simpler to represent portfolio construction as two sequential tasks. First, the correlation between the portfolio components is determined, and then the total weight of the portfolio is determined. The second problem seems to be fundamentally more important and for our small deposits it can be solved in the sense of optimizing the profit over a fixed period of time (under the condition of early termination of the portfolio trade when its equity drawdown exceeds a certain level)
I willingly believe that, but why is it necessary? It makes no sense to interpolate something between two ticks, because what happens between ticks is determined by a more detailed discrete stream of events at Level2 and Level3.
The functions used to model market and non-market processes are continuous and easier to understand. It is much harder to understand discrete entities. Besides, in a large set there is an effect of accumulation of properties of its members, it is like the opinion of the crowd about the price. It is essentially (aggregate opinion on price) in continuous time not discrete either. But decisions to buy and sell at such and such a price are discrete.
All these theories are very far from real life)
Everyone has their own life)
All these theories are very far from real life)
Not so far away. The measure of remoteness is characterised here:
and, more specifically for financial mathematics, here:
Quotes from Kendal https://www.mql5.com/ru/forum/368720/page30#comment_24266356
Where you can give the answer "one and a half diggers" and where you can't is all determined by the specific task at hand. After all, a digger can work for one and a half.
When constructing a portfolio of systems, new metrics emerge - the correlation matrix and the (auxiliary) level of significance of these correlations.
In my view, it is easier to represent portfolio construction as two sequential tasks. First, the correlation between the portfolio components is determined, and then the total weight of the portfolio is determined. The second problem is more important in principle. For our small deposits it can be solved in the sense of optimization of profit within a fixed period of time (under the condition of early termination of portfolio trading when the equity drawdown exceeds the specified level).
There is one more popular (for small deposits) approach when we trade using the "take it or leave it" method. It can be formalized as an exit after the deposit has either increased by the specified number of times or decreased by the specified number of times (margin call). If we don't add conditions related to time, the result will be trivial - the closer to zero volume is, the better (time tends to infinity). We need to either add an output when it reaches a predefined time or optimize the expected payoff to time ratio.
There is another popular (for small deposits) approach, where trading is done on a "take it or leave it" basis. It can be formalized as an exit when the deposit has either increased by a specified number of times or decreased by a specified number of times (margin call). If we don't add conditions related to time, the result will be trivial - the closer to zero volume is, the better (time tends to infinity). Either you need to add an output when it reaches a predetermined time, or optimize the expected payoff to time before the output.
In the under-read by many "player busting problem" and other martingales, there is an option to select the optimal multiplier (maximizing the number of rounds and/or the desired achievable bar).
The fact that the player with a finite capital goes bankrupt in an infinite game has been read and is depressed;
but the point that high risk with small deposits is optimal has not. That trading small is more rapid/reliable and that one of the paradoxes created.
In unreadable by many "the problem of ruining the player" and other martingales, there is an option to choose an optimal multiplier (maximizing the number of rounds and/or desired achievable bar).
The fact that the player with a finite capital goes bankrupt in an infinite game has been read and is depressed;
but the point that high risk with small deposits is optimal has not. As for the paradox that the small trading is faster/more reliable, it is one of the generated paradoxes.
The paradox is that losing games only reduces losses by increasing risk. You can't make a profit that way (from a losing game).
That sounds like the "did the sick man sweat before he died" joke to me ).
You can't "turn a losing economy into a profitable one without changing anything about it".)