Hopefully someone here has some knowledge in both finance and maths.
I am pondering on the existence/impossibility of a trading system (or algorithm) that ALWAYS ends up winning money, no matter how the price of a futures moves. That is, in a context where one can buy or sell (short) to make a profit.
If the trader has infinite funds, it's possible. He can setup some kind of martingale system and cancel every loss by making an opposite trade.
If the trader has limited funds, there's an intuitive proof that no system can win: if it existed, someone would have figured it out by now.
But I'm looking for a formal treatment of the question. Lots of papers deal with trading in a model in which prices movements are associated with probabilities, such as brownian movement and the like. But really, what I'm looking for is a proof that there's no algorithm that can beat ANY price movement. Meaning, for every trading algorithm, there exists a price movement in which the algorithm incurs a loss. Any references on the topic is appreciated.