Wasserstein-Based Systemic Risk Measures on Financial Networks: Theory, Computation, and Economic Implications via Optimal Transport

This paper develops a Wasserstein-based systemic risk framework for financial networks grounded in Optimal Transport theory. Unlike classical approaches that rely on variance-based or tail-risk measures, we model financial systems as probability distributions evolving over network structures and define systemic risk through transport costs between stressed and baseline states.

The core contribution is the introduction of a Wasserstein Systemic Risk Functional (WSRF), which quantifies how shocks propagate across interconnected institutions using transport geometry. By leveraging the dynamical formulation of optimal transport (e.g., Benamou–Brenier formulation), we interpret financial contagion as a flow of mass across a network, providing both a geometric and economic interpretation of systemic instability.

The paper combines:

rigorous mathematical formulation
network-based modeling
computational illustration

to demonstrate that Wasserstein-based metrics capture distributional shifts and contagion effects more effectively than traditional risk measures.