= Solution
A one-period <arbitrage> is a <portfolio> of initial-information-measurable holdings $(h_B,h_S)$ with value $V_t=h_BB_t+h_SS_t$ such that
$$
\boxed{V_0=0,\qquad V_1\geq0\text{ almost surely},\qquad\mathbb P(V_1>0)>0.}
$$
The holdings are fixed during the period, so this is a <self-financing strategy>. A <portfolio> costing a negative amount with nonnegative terminal value also gives an <arbitrage>: invest its initial surplus in the strictly positive <bank account> to obtain a zero-cost <portfolio> with a strict gain. The same definition applies when further traded assets are added.
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