If we knew exactly how the price was moving... - page 6
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Isn't that enough? Or do you have something better to say than that?
Normalisation and probability - do you see the difference, or do you think they are the same thing?
However, I no longer have the slightest desire to talk to you about anything.
Sorry, my mistake. Taking into account the spread on the synchronous BP should be:
p(tp) = (sl - spead) / (sl + tp)
p(sl) = (tp + spread) / (sl + tp)
However, I no longer have the slightest desire to talk to you about anything.
>> Likewise.
p(tp) = (tp - spread) / (sl + tp)
p(sl) = (sl + spead) / (sl + tp)
p(tp) + p(sl) = 1
the calculation is incorrect.
To calculate the probability of winning/losing it is necessary to know multivariate (more exactly, infinite-dimensional) a priori PDF of future price distribution (and do not say that the matstat is not applicable to time series, it is created for this purpose) W(x,n), where x - the event when the price reaches a certain maximum deviation from the entry point for a given (or unlimited) time n. If we also take into account discreteness of price axis, replacing integrals by summation, we obtain the following recurrence formulas for buying trade (for selling - mirror) (tp and sl are implied absolute levels)
P(tp) =S[n=1...N] {P(price>=tp for time from 0 to n)*P(price>sl for time from 0 to n-1)} =S[n=1...N] {S[Price=tp-spread... +oo](W(Price,n))*S[Price=sl+spread+1... +oo](W(Price,n-1))}
P(sl) =S[n=1...N] {P(price<=sl for time 0 to n)*P(price<tp for time 0 to n-1)} = S[n=1...N] {S[Price=-oo ... sl+spread](W(Price,n))*S[Price=-oo ... sl+spread+1](W(Price,n-1))}
where S[n=...]() is the summing operator, +-oo is how I draw the infinity
I.e. when calculating tp probability it should take into account the probability that sl has not worked earlier and vice versa.
So don't think it's that simple - multiply whatever you don't know and the result is ready. If it were that simple, I wouldn't ask.
To calculate the probability of win/loss it is necessary to know the multivariate (more precisely, the infinite dimensional) a priori PDF of the future price distribution ...
There is no need to count to infinity here. In fact, the problem is much more trivial, i.e. through an arithmetic progression. It's a very bearded problem.
alsu wrote(a) >>.
I.e. when calculating the probability of tp, the probability that sl did not work earlier must be taken into account and vice versa.
Well, it was stated by the Total Likelihood Theorem that p(tp) + p(sl) = 1. You can substitute the formulas for p(*) and check.
There's no need to count to infinity. In fact, the problem is much more trivial, i.e. through arithmetic progression. This problem is quite bearded.
Well, it was stated by the Total Likelihood Theorem that p(tp) + p(sl) = 1. You can substitute the formulas for p(*) and check.
It's obvious that the probability of losing + probability of winning = 1. The question is not about that, but about structuring these probabilities, getting them analytically based on market parameters. About bearded problem (if I understood correctly what we are talking about) - it is not applicable in this case, as it assumes uniform distributions, plus we do not know whether at a certain step this or that event or none will happen. By the way, I don't know how to calculate probabilities without taking into account the density of distribution (unless it's uniform). I was taught only this way:)
By the way, I don't know how to calculate probabilities without considering the density of the distribution (unless of course it's uniform). I was only taught that way:)
They taught you poorly (and where do they teach you - nerds in general and do they teach anything?):
probability (for right outcomes) = expected number of right outcomes / (expected number of right outcomes + expected number of wrong outcomes)
For frequency, the same formula, only instead of "expected", you have to substitute "real".
and no distribution densities or other nerdy nonsense.
You've been taught shit (and where do they teach you nerds, and do they teach you anything?):
probability (for right outcomes) = number of right outcomes / (number of right outcomes + number of wrong outcomes)
And no distribution densities and other nerdy nonsense.
Tikhonov started to teach, but not for long, he retired.
Again, your formula is correct, and yet trivial. And it reflects an estimate of the posterior probability, or rather, the frequency of winning, which is not the same thing, and its elements in those formulas that you cited above are calculated incorrectly. The correct formulas I wrote above.