  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.
