The market is a controlled dynamic system. - page 383
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With the birthday girl in the family.
Thank you! ))
1) If capital has a constant expected payoff, the system is unprofitable. A profitable system must have a rising expectation.
2) Martingale has constant expected payoff (13.1.3 point 1 from Korolyuk)
3) Equity of TS on SB is integral of Ito on position volume (for small increment of equity dc=v(t)dw(t), where v(t) is volume, and w(t) is a Wiener process)
4) Ito integral is a martingale (19.2.3 from Korolyuk) --> capital has constant expectation --> TS is unprofitable
1) true -- as a general statement
2) true -- as a general statement
3) false -- because TC is not obliged to perform operations at each step of SB, hence, the capital expectation is not equal to a constant. Recall here the super- and sub-martingales.
4) false - as a consequence of erroneous point 3
3) false -- because the TS is not obliged to perform transactions at each SB step
4) false -- as a consequence of erroneous p.3
Wrong. No transactions means only unchanged volume, but not unchanged equity - it is the price change (with non-zero volume) that is responsible. In a position with zero volume, of course the change in equity is zero for any change in price.
A basic TS that gives you the opportunity to make money on SB :
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When taking into account "thin" settings, leading to a complication of the basic TS, the share of losing trades is reduced. In the limit the share of losing trades tends to zero, but the TS becomes much more complex.
s.
Exactly this algorithm (with minor additions) was used by me in the branch"Random Walking" when demonstrating an opportunity to make money on SB
Here is just one example of the many examples given there:
Forum on trading, automated trading systems and testing trading strategies
Random Wandering :
Oleg avtomat, 2018.11.04 08:29
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Wrong. No transactions means only unchanged volume, but not unchanged capital - the price change is responsible for that (with non-zero volume). With zero position volume, of course the change in equity is zero for any change in price.
There is more to it than that. The very validity of using Ito's integral to determine capital in the context of applying TS to SB seems questionable.
There is more to it than that. The very validity of using Ito's integral to determine capital in the context of applying TS to SB seems questionable.
If we take a Wiener process as an SB, everything is OK. The measurability of v(t) with respect to the filtering set by this SB is sufficient there. Modern financial mathematics is based on a similar approach.
In the case of discrete SB everything is even simpler. The expectation of equity growth results in the product of volume and price growth (due to their independence by the definition of SB). If the expectation of price increase is zero (SB without trend), then the expectation of capital increase is also zero.
If you take a Wiener process as the SB, you are fine. It is sufficient to measure v(t) with respect to the filtration given by this SB. Modern financial mathematics is based on a similar approach.
In the case of discrete SB everything is even simpler. The expectation of equity growth results in the product of volume and price growth (due to their independence by the definition of SB). If price increment expectation is zero (SB without a trend), then equity increment expectation is also zero.
And where does TC lie in all this? It is absent. There is no place for it here.
Where is the TC in all this? It's not there. It has no place here.
It is she who generates the position of volume v(t) (a positive value corresponds to buying and a negative value corresponds to selling) based on the price before t. The point is that for the non-profitability of TS on SB it is enough that it cannot look into its future (that is how one should understand the measurability with respect to filtration) and its specific algorithm is unimportant.
The demonstration of a profitable TS on a fully known SB implementation is, in fact, a peek into the future.
It is it that generates a position of volume v(t) (a positive value corresponds to buying, and a negative one to selling), based on the price before t. The point is that for the non-profitability of the TS on SB it is enough that it cannot look into its future (that is how one should understand measurability in relation to filtering), and its specific algorithm is unimportant.
The demonstration of a profitable TS on a fully known SB implementation is, in fact, a peek into the future.
1) According to what algorithm"it's the one that generates a volume position v(t)" ?? Where do you take into account this algorithm ??? You assume that it is absolutely random ! But that's not the case at all !!!
2) Here is where you are completely wrong. TC works without looking into the future. TC uses only past values and the current value. I can demonstrate this in step-by-step mode by inputting rnd() updated at each step.
1) By what algorithm"It is it that generates the position of the volume v(t)" ??? Where do you account for this algorithm ??? You accept that it is completely random. But that's not the case at all !!!
2) Here is where you are completely wrong. TS works without looking into the future. TC uses only past values and the current value. I can demonstrate this in stepwise mode by feeding the rnd() updated at each step to the input.
Oleg, if the deterministic algorithm has SB as input, then the output is also SB. Except of a different distribution. By the way, deterministic algorithms always are cyclic. This is already from Thuring's :-)