  We give an elementary proof of the celebrated Bichteler-Dellacherie Theorem
which states that the class of stochastic processes $S$ allowing for a useful
integration theory consists precisely of those processes which can be written
in the form $S=M+A$, where $M$ is a local martingale and $A$ is a finite
variation process. In other words, $S$ is a good integrator if and only if it
is a semi-martingale. We obtain this decomposition rather directly from an
elementary discrete-time Doob-Meyer decomposition. By passing to convex
combinations we obtain a direct construction of the continuous time
decomposition, which then yields the desired decomposition. As a by-product of
our proof we obtain a characterization of semi-martingales in terms of a
variant of \emph{no free lunch}, thus extending a result from [DeSc94].
