\ 0 \leq t\leq \bar T \right\}$ the continuous exchange rate process between currency $i$ and $j$. Here $S^{i,j}(t)$ denotes the price of one unit of currency $i$ in units of currency $j$, meaning that, e.g. for $i=USD$ and $j=EUR$ and $S_t^{i,j}=0.92$ we have, in line with the standard FORDOM convention, that the price of one USD is $0.92$ EUR at time $t$.

Let us follow [@bookplaten10] and [@currencyplaten06] and introduce a family of primary security account processes via $$\begin{aligned}
B^{i,j}(t)=S^{i,j}(t)B^j(t), \ 0\leq t\leq \bar T\end{aligned}$$ for $i\neq j$. Obviously, for $i=j$ we have $B^{i,i}(t)=B^{i}(t)$. We take the perspective of a generic currency referenced with superscript $i$ and introduce the vector of money market accounts of the form $\boldsymbol{B}^i(t)=\left(B^{i,1}(t),...,B^{i,N}(t)\right)$, $i=1,...,N$. Given this vector of primary security accounts, an investor may trade on them. This is represented by introducing a family of predictable $\boldsymbol{B}^i$-integrable stochastic processes $\boldsymbol\delta=\left\{\boldsymbol\delta (t)=\left(\delta_1(t),...,\delta_N(t)\right), \ 0 \leq t\leq \bar T \right\}$ for $i=1,...,N$, called strategies. Each $\delta_j(t)\in {\mathbb{R}}$ denotes the number of units that an agent holds in the $j$-th primary security account at time $t$. Let us introduce the process ${\mathtt{V}}^{i,\delta}=\left\{\mathtt{V}^{i,\delta}(t), \ 0 \leq t\leq \bar T \right\}$, which describes the value process in $i$-th currency 