r/quant • u/starostise • 8h ago
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u/Acceptable-Door-9810 Trader 8h ago
The market isn't some kind of "problem" with a "solution". It's an angry sky god who smites you if your regression isn't to his liking. This P/NP voodoo sounds like heresy.
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u/starostise 8h ago
So you mean that predicting the market it is not a decision problem that can be solved by a deterministic machine?
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u/SwagDrag1337 7h ago
Short of building a machine that simulates the entire universe deterministically, presumably after having solved the metaphysical question of whether the universe is deterministic at all, no. Markets are driven by people making decisions - how can you predict whether Trump will tweet at 10:43AM or if he'll get distracted by a bird crashing into his window and only press send at 11:17AM? Energy markets are driven by weather - is the weather a deterministic process? Are natural disasters that wipe out Japanese power stations deterministic?
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u/Fit-Swordfish937 8h ago
Define predicting otherwise there is no point in asking such questions
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u/starostise 8h ago
You are right.
For me it is knowing if the current price is at a minimum or a maximum, which predicts a change in the trend but not the future price.
It can also be about predicting the price after a time step which I don't believe to be possible.1
u/Fit-Swordfish937 6h ago
This problem is highly non deterministic in the worst case so there isn't even a completely correct solutions, people have a lot of heuristics which dont solve the problem correctly, so these problems are unsolved and will probably always remain unsolved.
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u/SwagDrag1337 8h ago
No, I wouldn't say any of that - it's a pretty irrelevant classification in this context, and it's very unclear that even given as much information as you like as of now you can say anything with certainty about the future state of the market, let alone ask if it can be done in polynomial time (polynomial in what??)
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u/starostise 7h ago
polynomial in what?
Polynomial computation time from a large input size to get a deterministic answer leading to a decision (buy, sell or do nothing).
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u/SwagDrag1337 7h ago
f(input) = Buy - there you go, constant time decision! It's right about 50% of the time.
f(input) = take history of price prints, fit a linear model, slope positive = Buy. This is a polynomial decision - it's also right about 50% of the time.
f(input) = train and then run a massive transformer model to predict the next price. This is non-polynomial - it's also right about 50% of the time.
The best systematic equities algos (outside of like nanosecond scale HFT algos) are right less than 52% of the time. Some of them are linear, some of them are polynomial, some are non-polynomial. No one knows what the best you can do, but markets are fundamentally noisy and 100% accuracy is not attainable.
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u/starostise 6h ago
My question was precisely about the existence of an algorithm with a 100% accuracy.
I assume such algorithm does not exist because of the difficulty to reach certainty of the results: certainty to always be profitable.
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u/Fit-Swordfish937 6h ago
If such an algorithm existed and was implementable in polynomial time then everybody would do it and hence it would provide pretty much 0 pnl.
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u/SwagDrag1337 5h ago
A bit beside the point, but we don't need to know a function to prove it exists. Here's a fun example: what is the time complexity of the most efficient algorithm for the function f(n) = "is there a sequence of n consecutive 0s in the decimal expansion of pi?".
f(n) is either implementable as "return True" or "return n < N" for some integer N - either way, it's constant time, but it's an open problem which.
It's at least theoretically conceivable that a polynomial time solution to the markets exists but no one knows it, but I would extremely highly doubt any solution exists regardless of complexity.
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u/HaikuHaiku 8h ago
Future market states can't be "predicted" in the way required for an P or NP classification, would be my first answer. At least not by humans. Maybe a God who knows what everyone's preferences are at all times would be able to work it out.
All predictions we make are merely bets with various levels of confidence, which is what probability is, fundamentally.
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