If $A=\operatorname{Im}V=\mathbb R^n$, the symmetric covariance matrix $V$ is positive definite. For every nonzero $H$, the scalar $H\cdot P_1$ is normal with variance $H^TVH>0$, so it has positive probability of being negative. It cannot be an arbitrage payoff. The zero portfolio provides no strict gain, proving absence of arbitrage.


Solution

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

 Solution (source code)