Past exam of the mathematics course of the University of Cambridge / 2020 / ii / Paper 2 / 29K / iv

There is no arbitrage. Indeed, part (iii) supplies an equivalent martingale measure, so the fundamental theorem of asset pricing implies absence of arbitrage. Directly, the discounted terminal value of a zero-cost admissible self-financing strategy is a ${\mathbb{P}}^{\ast }$-martingale with mean zero; it cannot be nonnegative almost surely and positive with positive probability.