Related papers: Clearing Sections of Lattice Liability Networks
Assessing the resilience of the economy requires accounting for its intrinsic multi-layer nature, by assessing for instance how disruptions at the firm level spread through the production network and propagate to the banking sector. Methods…
We consider a network of sellers, each selling a single product, where the graph structure represents pair-wise complementarities between products. We study how the network structure affects revenue and social welfare of equilibria of the…
We study the structure of the set of priority-neutral matchings. These matchings, introduced by Reny (AER, 2022), generalize stable matchings by allowing for priority violations in a principled way that enables Pareto-improvements to stable…
The fundamental concept of applying the system methodology to network analysis declares that network architecture should take into account services and applications which this network provides and supports. This work introduces a formal…
The structure of the supply chain network has important implications for modelling economic systems, from growth trajectories to responses to shocks or natural disasters. However, reconstructing firm-to-firm networks from available…
The complexity of financial markets arise from the strategic interactions among agents trading stocks, which manifest in the form of vibrant correlation patterns among stock prices. Over the past few decades, complex financial markets have…
The 2008 financial crisis illustrated the need for a thorough, functional understanding of systemic risk in strongly interconnected financial structures. Dynamic processes on complex networks being intrinsically difficult, most recent…
This work develops a flexible and mathematically sound framework for the design and analysis of graph scattering networks with variable branching ratios and generic functional calculus filters. Spectrally-agnostic stability guarantees for…
We introduce an event based framework of directional changes and overshoots to map continuous financial data into the so-called Intrinsic Network - a state based discretisation of intrinsically dissected time series. Defining a method for…
Increasingly sophisticated mathematical modelling processes from Machine Learning are being used to analyse complex data. However, the performance and explainability of these models within practical critical systems requires a rigorous and…
We introduce a geometric theory of payment channel networks that centers the polytope $W_G$ of feasible wealth distributions; liquidity states $L_G$ project onto $W_G$ via strict circulations. A payment is feasible iff the post-transfer…
The network inference problem consists of reconstructing the edge set of a network given traces representing the chronology of infection times as epidemics spread through the network. This problem is a paradigmatic representative of…
This note reformulates certain classical combinatorial duality theorems in the context of order lattices. For source-target networks, we generalize bottleneck path-cut and flow-cut duality results to edges with capacities in a distributive…
We introduce a simple class of distribution networks which withstand damage by being repairable instead of redundant. We prove a lower bound for the expected cost of repair, and show that for networks on the square and triangular lattice,…
In this paper we present formulas for the valuation of debt and equity of firms in a financial network under comonotonic endowments. We demonstrate that the comonotonic setting provides a lower bound and Jensen's inequality provides an…
We propose a general integrable lattice system involving some free parameters, which contains known integrable lattice systems such as the Ablowitz-Ladik discretization of the nonlinear Schr\"odinger (NLS) equation as special cases. With a…
Many complex networks display remarkable resilience under external perturbations, internal failures and environmental changes, yet they can swiftly deteriorate into dysfunction upon the removal of a few keystone nodes. Discovering theories…
The vast corpus of physics equations forms an implicit network of mathematical relationships that traditional analysis cannot fully explore. This work introduces a graph-based framework combining neural networks with symbolic analysis to…
Many social, technological, biological, and economical systems are best described by weighted networks, whose properties and dynamics depend not only on their structures but also on the connection weights among their nodes. However, most…
Over the last two decades, financial systems have been studied and analysed from the perspective of complex networks, where the nodes and edges in the network represent the various financial components and the strengths of correlations…