A portfolio $H\in\mathbb R^n$ is an <arbitrage> when $H\cdot P_0\leq0$, $H\cdot P_1\geq0$ 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 $H\cdot P_0=0$, $H\cdot P_1\geq0$ almost surely, and the terminal inequality is strict with positive probability.

Solution

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

A terminal-consumption arbitrage has zero initial cost and a nonnegative terminal payoff that is strictly positive with positive probability. Allowing negative initial cost gives the broader one-period notion in which some consumption may occur immediately.


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 Incoming links: Terminal-consumption arbitrage