with multiple maturities by considering each clearing date as a different asset. All of these works, however, only consider clearing at discrete times. [@sonin2017] presents a continuous-time clearing model that exactly replicates the static Eisenberg-Noe framework. In this work we will present both discrete and continuous-time clearing models. However, our emphasis will be on the derivation and the characterization of the continuous-time model. This in part is motivated by the prospect of unification with the mean-field models as well as traditional financial models which typically employ continuous-time models. Additionally, as we will demonstrate, the continuous-time framework no longer requires monotonicity for existence and uniqueness which is generally assumed for static and discrete-time systems. This is valuable for future works that may model network formation and payments as a non-cooperative game; such games may not satisfy the strong monotonicity assumptions usually considered in static and discrete-time systems, but would likely satisfy the sufficient conditions for the continuous-time framework.

The organization of this paper is as follows. In Section \[sec:setting\] we will provide a review of the static Eisenberg-Noe framework. Of particular interest, in this section, we consider the clearing to be in terms of the equity and losses of the firms, 