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

For initial capital zero and a predictable strategy $H$, let $C_t^{0,H}$ denote consumption after the time-$t$ portfolio payoff and before choosing the next holdings. An investment-consumption arbitrage haswith strictly positive consumption at some date with positive probability. A terminal-consumption arbitrage is a finite-horizon such strategy whose consumption is zero before its terminal date $T$, while $C_T^{0,H}\ge 0$ almost surely and $\mathbb{P}(C_T^{0,H}>0)>0$.