Zero-capital nonnegative wealth under a local deflator
= Zero-capital nonnegative wealth under a local deflator
{title2=$V_0=0,\ V\ge0\Longrightarrow V\equiv0$}
For a <self-financing portfolio> whose product with a strictly positive local deflator is a <local martingale>, nonnegative wealth makes that product a <supermartingale>. Starting from zero forces it to vanish almost surely at each time. Continuous paths then give simultaneous vanishing at every time on one probability-one event.