  A well known result in stochastic analysis reads as follows: for an
$\mathbb{R}$-valued super-martingale $X = (X_t)_{0\leq t \leq T}$ such that the
terminal value $X_T$ is non-negative, we have that the entire process $X$ is
non-negative. An analogous result holds true in the no arbitrage theory of
mathematical finance: under the assumption of no arbitrage, a portfolio process
$x+(H\cdot S)$ verifying $x+(H\cdot S)_T\geq 0$ also satisfies $x+(H\cdot
S)_t\geq 0,$ for all $0 \leq t \leq T$.
  In the present paper we derive an analogous result in the presence of
transaction costs. A counter-example reveals that the consideration of
transaction costs makes things more delicate than in the frictionless setting.
