also been considered for studying financial contagion and systemic risk. [@fouque2013illustrated] provides a model of agents who revert to the ensemble mean to provide understanding of “systemic risk events” in which many firms fail. Similar mean field diffusion models without controls were studied in, e.g., [@fouque2013stability; @garnier2013a; @garnier2013b]. In contrast, mean field and stochastic games have been proposed for the study of systemic risk in, e.g., [@fouque2015meanfield; @carmona2016delay]. In such models the firms are allowed to borrow from (or lend to) a central bank, the amount of which is optimized to minimize a quadratic cost function. Thus the choice of borrowing and lending provides an optimal control problem beyond the simpler mean field model of [@fouque2013illustrated]. [@NS17] proposes a separate particle system model with mean field interactions.

The current work will focus on adding the time dynamics, which make the mean field models attractive, to the interbank network approach. In fact, the conclusion of [@EN01] provides a discussion of future extensions, one of which is the inclusion of multiple clearing dates. This has been studied directly in [@CC15; @ferrara16]. Additionally, [@KV16] considers a similar approach to model financial networks with multiple maturities. [@feinstein2017currency] further provides another approach to financial networks 