Past exam of the mathematics course of the University of Cambridge / 2019 / iii / Paper 211 / 4 / b

A numéraire strategy $\eta$ has zero consumption and strictly positive wealthat every date. Given an investment-consumption arbitrage $H$, retain its holdings and invest each nonnegative consumption $C_s^{0,H}$ in the numéraire. Withthe self-financing identity for $\eta$ gives zero intermediate consumption for $K$. At a deterministic $T$ after a date at which positive consumption occurs with positive probability, liquidating givesIt is strictly positive with positive probability. Hence $K$ is a terminal-consumption arbitrage.