Sharp Transitions and Systemic Risk in Sparse Financial Networks

Riley James Bendel

Papers from arXiv.org

Abstract: We study contagion and systemic risk in sparse financial networks with balance-sheet interactions on a directed random graph. Each institution has homogeneous liabilities and equity, and exposures along outgoing edges are split equally across counterparties. A linear fraction of institutions have zero out-degree in sparse digraphs; we adopt an external-liability convention that makes the exposure mapping well-defined without altering propagation. We isolate a single-hit transmission mechanism and encode it by a sender-truncated subgraph G_sh. We define adversarial and random systemic events with shock size k_n = c log n and systemic fraction epsilon n. In the subcritical regime rho_out

Date: 2026-01
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