Past exam of the mathematics course of the University of Cambridge / 2023 / iii / Paper 211 / 1 / a

A portfolio $H\in {\mathbb{R}}^n$ is an arbitrage when $H\cdot P_0\le 0$, $H\cdot P_1\ge 0$ almost surely, and at least one inequality supplies a strict gain: either $H\cdot P_0<0$ or $\mathbb{P}(H\cdot P_1>0)>0$. It is a terminal-consumption arbitrage when $H\cdot P_0=0$, $H\cdot P_1\ge 0$ almost surely, and the terminal inequality is strict with positive probability.