clearing wealths driven by $(dc,dL)$ when $c(t) = \int_0^t dc(s)$ is an Itô process and $L(t) = \int_0^t dL(s)$ is deterministic and continuous (e.g., $dL$ does not include any Dirac delta functions). This setting, and the results on the continuous-time Eisenberg-Noe model, can be extended to the case in which the cash flows and liabilities are additionally functions of the wealths $V$. For simplicity, in this section we will restrict ourselves so that the parameters are independent of the current wealths. In order to construct a continuous-time differential system, we will consider again the discrete-time setting with explicit time steps ${{\Delta t}}$.

\[ass:society\] The cash flows $c$ are defined by the Itô stochastic differential equation $dc(t) = \mu(t,c(t))dt + \sigma(t,c(t))dW(t)$ for $(n+1)$-vector of Brownian motions $W$ over some filtered probability space $(\Omega,{\mathcal{F}},({\mathcal{F}}_t)_{t \in {\mathbb{T}}},{\mathbb{P}})$. Additionally, the drift and diffusion functions $\mu: {\mathbb{T}}\times {\mathbb{R}}^{n+1} \to {\mathbb{R}}^{n+1}$ and $\sigma: {\mathbb{T}}\times {\mathbb{R}}^{n+1} \to {\mathbb{R}}^{(n+1) \times (n+1)}$ are jointly continuous and satisfy the linear growth and Lipschitz continuous conditions, i.e., there exist constants $C,D > 0$ such that for all times $t \in {\mathbb{T}}$ and cash flows $c,d \in {\mathbb{R}}^{n+1}$ $$\begin{aligned}
\|\mu(t,c)\|_1 + \|\sigma(t,c)\|_1^{op} &\leq C(1 + \|c\|_1)\\
\|\mu(t,c) - \mu(t,d)\|_1 + \|\sigma(t,c) - 