payments. In [@EN01] results for the existence and uniqueness of the clearing payments (and thus for the clearing wealths as well) are provided. In fact, it can be shown that there exists a unique clearing solution in the Eisenberg-Noe framework so long as $L_{i0} > 0$ for all firms $i \in {\mathcal{N}}$. We will take advantage of this result later in this paper. This is a reasonable assumption (as discussed in, e.g., [@GY14]) as obligations to society include, e.g., deposits to the banks.

Discrete-time clearing systems {#sec:discrete}
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Consider now a discrete set of clearing times ${\mathbb{T}}$, e.g., ${\mathbb{T}}= \{0,1,\dots,T\}$ for some (finite) terminal time $T < \infty$ or ${\mathbb{T}}= {\mathbb{N}}$. Such a setting is presented in [@CC15]. For processes we will use the notation from [@cont2013ito] such that the process $Z: {\mathbb{T}}\to {\mathbb{R}}^n$ has value of $Z(t)$ at time $t \in {\mathbb{T}}$ and history $Z_t := (Z(s))_{s = 0}^t$.

(0,9.5) rectangle (6,10) node\[pos=.5\][**Balance Sheet**]{}; (0,9) rectangle (3,9.5) node\[pos=.5\][**Assets**]{}; (3,9) rectangle (6,9.5) node\[pos=.5\][**Liabilities**]{};

(0,7) rectangle (3,9) node\[pos=.5,style=[align=center]{}\][Cash-Flow @ $t = 0$\
$x_i(0)$]{}; (0,6) rectangle (3,7) node\[pos=.5,style=[align=center]{}\][Cash-Flow @ $t = 1$\
$x_i(1)$]{}; (0,2) rectangle (3,6) node\[pos=.5,style=[align=center]{}\][Interbank @ $t = 0$\
$\sum_{j = 1}^n \pi_{ji}(0)p_j(0)$]{}; (0,0) rectangle (3,2) node\[pos=.5,style=[align=center]{}\][Interbank @ $t = 