 Solution

A one-period arbitrage is a portfolio of initial-information-measurable holdings $(h_B,h_S)$ with value $V_t=h_B{B}_t+h_S{S}_t$ such thatThe 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.