price processes $\hat{B}^{j}$ form ${\mathbb{P}}$-local martingales. Even more, they are non-negative ${\mathbb{P}}$-local martingales. Hence, due to Fatou’s lemma, they are also ${\mathbb{P}}$-supermartingales. Analogously, we also have that benchmarked non-negative portfolio values $\hat{{\mathtt{V}}}^{\delta}(t):={{\mathtt{V}}}^{i,\delta}(t)/D^i(t)$ form ${\mathbb{P}}$-supermartingales. Besides the exclusion of forms of economically meaningful arbitrage, which are equivalent to the explosion of the GOP, forms of classical arbitrage that are excluded under classical no-arbitrage assumptions may exist in our model, see e.g. [@Loewenstein00].

Let us now introduce for the $i$-th currency denomination the Radon-Nikodym derivative process, denoted by $\Lambda^i=\left\{\Lambda^i(t), \ 0\leq t \leq \bar{T}\right\}$, by setting $$\begin{aligned}
\Lambda^i(t)=\frac{\hat{B}^{i}(t)}{\hat{B}^{i}(0)},\quad i=1,\ldots, N\label{radoni}.\end{aligned}$$ This is the risk neutral density for the putative risk-neutral measure $\mathbb{Q}^i$ of the $i$-th currency denomination. It arises e.g. when we consider replicable claims and assume the existence of an equivalent risk neutral probability measure $\mathbb{Q}^i$. As each $\Lambda^i$ equals the corresponding benchmarked savings account $\hat{B}^{i}$ (up to a constant factor), it is clear that $\Lambda^i$ is a ${\mathbb{P}}$-local martingale, for $i=1,\ldots, N$. The classical assumption in the foreign exchange literature that there exists an equivalent risk-neutral probability measure for each currency denomination, corresponds to the requirement that each process $\Lambda^i$ is a true martingale for $i=1,\ldots, N$. Such a requirement 