We prove that Theorem 4.16 in [1] is false by constructing a strategy that generates $ (FLVR)_{ \mathcal{H}(\mathbb{G})} $. However, we success to prove that the no arbitrage property still holds when the agent only plays with strategies belonging to the admissible set called buy-and-hold.
Keywords: arbitrage; enlargement of filtration; no free lunch vanishing risk; optimal portfolio.