On a fundamental statistical edge principle
This paper establishes that conditioning the probability of execution of new orders on the self-generated historical trading information (HTI) of a trading strategy is a necessary condition for a statistical trading edge. It is shown, in particular, that, given any trading strategy S that does not use its own HTI, it is always possible to construct a new strategy S* that yields a systematically increasing improvement over S in terms of profit and loss (PnL) by using the self-generated HTI. This holds true under rather general conditions that are frequently met in practice, and it is proven through a decision mechanism specifically designed to formally prove this idea. Simulations and real-world trading evidence are included for validation and illustration, respectively.
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