We analyze how errors in interbank liabilities affect the clearing vector in financial systems.
problem Estimation errors in interbank liabilities can lead to inaccuracies in the clearing vector, impacting risk assessments.
method We quantify the sensitivity of the clearing vector to estimation errors in the interbank liabilities matrix using a basis for permissible perturbations.
result We derive analytical solutions for the maximal deviations of the clearing vector and compute upper bounds for worst-case perturbations.
Model financial contagion with dynamic interbank liabilities.
problem Model financial contagion with time dynamics of interbank liabilities.
method Generalized Eisenberg-Noe model with time dynamics, separating cash and capital accounts.
result Distinguish between delinquency and default, insolvency and illiquidity.
Paper finds efficient algorithms for computing fixed points in financial networks.
problem Computing fixed points in complex financial networks with potential defaults.
method Tarski's theorem and polynomial-time algorithms for minimal and maximal fixed points.
result Efficient algorithms for computing minimal and maximal fixed points in financial networks.
Study dual representations for quasiconvex systemic risk measures.
problem Finding dual representations for quasiconvex systemic risk measures.
method Abstract infinite-dimensional setting, explicit formula for penalty function, nonstandard minimax inequality.
result Explicit formula for the penalty function of quasiconvex compositions.
The paper analyzes financial networks with default charges and defines a model using fixpoint problems.
problem Modeling systemic risk in interbank networks with crossholdings and default charges.
method Mixed integer-linear programming and Gaussian elimination algorithm for computing clearing pairs.
result Developed methods to compute maximal and minimal clearing pairs.
Unified framework for complex financial networks using lattice theory.
problem Complex financial networks with multiple currencies and dependencies.
method Recast classical financial clearing model into lattice liability networks.
result Lattice-valued clearing sections form a complete lattice, enabling tractable analysis.
A new model calculates optimal clearing payments in dynamic financial networks.
problem Determining fair clearing payments in networks with potential defaults.
method Extends Eisenberg-Noe model to multiple time periods, solving linear programs for optimal payments.
result Proves the model satisfies the priority of debt claims requirement and finds unique optimal payments.
Study how contingent payments affect financial network stability.
problem Impact of contingent payments on systemic risk in financial networks.
method Developed static and dynamic models of financial contagion to analyze the effects of contingent payments on wealth distribution and network stability.
result Dynamic framework provides a solution to problems not defined in the static framework.
A new method for clearing liability networks using sheaves on directed hypergraphs.
problem Clearing in liability networks using a novel mathematical approach.
method Associate a liability sheaf on a directed hypergraph to a liability network, identifying clearing configurations as global sections of this sheaf.
result Clearing configurations are precisely the global sections of the sheaf, and the sheaf construction is functorial under change of coefficient category.
Model connects financial contagion models to mean field analysis.
problem Systemic risk in financial networks.
method Combines Eisenberg-Noe and mean field models.
result Mean field limit derived from finite bank system.
Modeling financial networks to predict systemic crises.
problem Predicting systemic financial crises in complex networks.
method Developed inhomogeneous random financial networks (IRFNs) to model bank interactions.
result Found a condition for a locally tree-like independence (LTI) property, leading to fixed point equations for system equilibrium.
The paper studies the convergence of SAA for systemic risk measures.
problem Theoretical convergence of SAA for set-valued systemic risk measures.
method General theory and specific case study with mixed-integer programming formulations.
result Theoretical convergence results for SAA under Wijsman and Hausdorff topologies.
The paper presents formulas for valuing debt and equity in interconnected firms with comonotonic endowments.
problem Valuation of debt and equity in interconnected firms with comonotonic endowments.
method Formulas derived under comonotonic setting, demonstrating lower and upper bounds using Jensen's inequality.
result The comonotonic setting provides a lower bound and Jensen's inequality an upper bound to the price of debt.
New method to determine parabolic surfaces invariant under Killing fields.
problem Characterizing parabolic invariant surfaces.
method Clear and practical characterization method for invariant surfaces.
result A new way to determine parabolicity of invariant surfaces.
Mixed-integer programming solves systemic risk measures for interdependent financial systems.
problem Computing systemic risk measures for interdependent financial systems with joint risk considerations.
method Proposes a mixed-integer programming problem to compute clearing vectors in a Rogers-Veraart network model with unrestricted sign operating cash flows.
result The proposed mixed-integer programming problem can compute systemic risk measures for interdependent financial systems.
The divergence-like operator on an odd symplectic superspace which acts invariantly on a specially chosen odd vector field is considered. This operator is used to construct an odd invariant semidensity in a geometrically clear way. The formula for this semidensity is similar to the formula of the mean curvature of hype…
In the present paper we construct differential invariants for generic rank 2 vector distributions on n-dimensional manifold. In the case n=5 (the first case containing functional parameters) E. Cartan found in 1910 the covariant fourth-order tensor invariant for such distributions, using his "reduction-prolongation" pr…
This paper aims at setting out the basics of Z-graded manifolds theory. We introduce Z-graded manifolds from local models and give some of their properties. The requirement to work with a completed graded symmetric algebra to define functions is made clear. Moreover, we define vector fields and ex…
Study claims trading to rescue banks in distress.
problem Rescue a bank in distress using claims trading.
method Formalize claims trading in financial networks, study decision and optimization problems, provide efficient algorithms for creditor-positive trades.
result No trade can strictly improve both banks' assets; provide efficient algorithms for creditor-positive trades.
We propose a model for the credit and liquidity risks faced by clearing members of Central Counterparty Clearing houses (CCPs). This model aims to capture the features of: gap risk; feedback between clearing member default, market volatility and margining requirements; the different risks faced by various types of mark…
Unified model for network risks, including bilateral and central clearing, with practical applications.
problem Managing risks in financial networks with multiple trading types.
method Developed a one-period XVA model with explicit formulas for various quantities.
result Illustrated practical uses for stress testing and portfolio optimization.
A Nash game theory approach allocates capital requirements among financial institutions.
problem Allocating systemic risk measures among financial institutions.
method Proposes a Nash allocation rule inspired by game theory.
result Provides sufficient conditions for the existence and uniqueness of Nash allocation rules.
Our work proves robustness of embedding schemes to discrete changes in text.
problem Discrete changes in text, like replacing a word, affect model robustness.
method Formal proofs and quantitative bounds for embedding schemes (concatenation, TF-IDF, Paragraph Vector).
result Embedding schemes are robust to discrete changes in text with Hölder or Lipschitz properties.
Optimal control solves multi-period liability clearing problems.
problem Clearing liabilities among entities over multiple periods.
method Formulated as a convex optimal control problem, solved using convex costs and constraints.
result Solves the problem of clearing liabilities among entities over multiple periods.
The financial crisis showed the importance of measuring, allocating and regulating systemic risk. Recently, the systemic risk measures that can be decomposed into an aggregation function and a scalar measure of risk, received a lot of attention. In this framework, capital allocations are added after aggregation and can…
Paper introduces Cycles Protocol to integrate trade credit into market clearing.
problem Liquidity embedded in trade credit outside formal settlement infrastructures.
method Distributed, multilateral clearing mechanism based on double-entry accounting.
result Cycles Protocol maximizes balance sheet compression without redistributing counterparty risk.
A two-step market clearing method for local energy trading among prosumers and consumers.
problem Integrating distributed energy resources into local energy markets.
method Feeder-based market with Two-StepMarket Clearing (2SMC) mechanism.
result Maximizes market surplus and correct incentives for prosumers and consumers.
Unified approach to data processing using gauge theory.
problem Data representation and analysis with consistent symmetry.
method Geometric gauge theory for discrete vector bundles.
result Unified understanding of heat kernel properties and data transformation.
FrequentNet uses frequency domain basis vectors for image classification, making models more interpretable and efficient.
problem Image classification models are often complex and hard to interpret.
method FrequentNet selects filter vectors from frequency domain basis vectors instead of training them with back propagation.
result The method improves interpretability and efficiency of image classification models.
The paper learns optimal auction prices by matching supply and demand.
problem Predicting optimal prices for market clearing.
method Learning framework using auction data to optimize revenue.
result Learned prices outperform other models in auctions and markets.
The paper examines clearing payments in financial networks to prevent cascaded defaults.
problem Cascaded defaults in financial networks under the proportionality rule.
method Analysis of clearing model under pro-rated payments, derivation of necessary and sufficient conditions for clearing payments, convex optimization problems for computation.
result Clearing payments can be computed by solving convex optimization problems, reducing overall system loss by lifting the proportionality rule.
Paper proposes a decentralized payment clearing system using blockchain and optimal bidding strategies.
problem Default contagion in a network of smart contracts cleared through blockchain.
method Constructs a decentralized clearing mechanism using blockchain and optimal bidding strategies.
result Proves existence and uniqueness of equilibrium clearing condition for terminal net worths.
CLEAR calibrates both aleatoric and epistemic uncertainties for better predictive intervals.
problem Balanced uncertainty quantification for reliable predictive modeling.
method CLEAR uses two parameters, γ1 and γ2, to combine aleatoric and epistemic uncertainties.
result Clear achieves significant improvements in interval width and coverage.
This paper develops an XVA (costs) analysis of centrally cleared trading, parallel to the one that has been developed in the last years for bilateral transactions. We introduce a dynamic framework that incorporates the sequence of cash-flows involved in the waterfall of resources of a clearing house. The total cost of …
Proposes a model for clearing prices in financial markets due to margin calls.
problem Determining prices in financial markets following margin calls and short squeezes.
method Developed an explicit formulation for clearing prices after margin calls and short squeezes.
result Identified a threshold short interest ratio leading to discontinuity in clearing prices.
KineticSim accelerates financial market simulations 3406x over CPU.
problem Simulating financial markets at scale with multi-agent models is bottlenecked by sequential processing and GPU kernel overhead.
method Formalized and implemented a reusable parallel design pattern for iterative multi-agent reductions in thread-block shared memory.
result Achieved a peak throughput of over 54.7 billion agent-events per second, delivering 3406x speedup over CPU.
KineticSim: A lightweight, high-performance execution engine for real-time market simulators
problem Simulating financial markets at scale with multi-agent models
method Reusable parallel design pattern: persistent, state-carrying clearing for iterative multi-agent reductions
result Reduces per-step critical-path depth from Theta(L+A) to Theta(log L + ceil(A/L))
A mathematical model describes deforming manifolds with precise vectors and fields.
problem Modeling and describing the deformation of complex manifolds in practical applications.
method Proposes a modified differential dynamic model with constraints on spatial and temporal continuity, presenting deforming vector and field.
result Demonstrates the effectiveness of an autonomous deforming field in data dimension reduction tasks.
CLEAR learns causal graphs from attention in recommender systems to explain user behavior.
problem Understanding why specific recommendations are made in recommender systems.
method CLEAR learns session-specific causal graphs from attention in pre-trained neural recommenders, addressing latent confounders.
result CLEAR provides counterfactual explanations that are shorter and more effective than naive methods.
Eigen-decomposition simplifies quadratic programming with equality constraints.
problem Optimizing solutions under linear equality constraints in quadratic programming.
method Eigenvalue decomposition of the quadratic term matrix to project optimal solutions.
result Established a linear mapping between EQP formulations with and without diagonalized Q. Improved hardness results for clearing payments in financial networks with CDSs.
problem Determining clearing payments in financial networks with CDSs after financial shocks.
method Analyzing computational complexity of clearing problems, showing PPAD-hardness and FIXP-completeness improvements.
result PPAD-hardness of clearing problem significantly improved to ε ≈ 0.101.
FinanceBench benchmarks LLMs on financial QA, revealing limitations.
problem Evaluating LLMs' performance on financial question answering.
method Developed a comprehensive test suite (FinanceBench) with 10,231 questions, tested 16 models, and manually reviewed answers.
result Existing LLMs have significant limitations for financial QA, especially GPT-4-Turbo.
We break down transformer embeddings into interpretable components revealing hidden geometric structures.
problem Understanding the hidden geometry and interpretability of transformer models.
method Decomposed transformer embeddings into position, context, and residual components.
result Pervasive mathematical structure in transformer embeddings, including position and context vectors.
Paper models financial contagion with fire sales and borrowing.
problem Financial contagion and systemic risk in interconnected financial networks.
method Modeling financial contagion in a network with fire sales and borrowing, considering both uncollateralized and collateralized loans.
result Existence and uniqueness of clearing solutions (payments, liquidations, and borrowing) are provided under certain conditions, and these solutions are Nash equilibria.
New approach solves complex electricity market clearing with UPP and block orders.
problem Complex market clearing with UPP and block orders.
method Equivalent UPP formulation leads to mixed-integer linear program.
result Exact solution without approximation, using real market data.
Blockchain markets with paid-priority trading can lead to biased prices and reduced liquidity.
problem Discrete clearing and paid-priority in blockchain markets lead to biased prices and reduced liquidity.
method Developed a model to evaluate the viability of blockchain markets under discrete clearing and paid-priority.
result Paid-priority ordering induces endogenous selection, leading to biased prices and reduced liquidity.
We consider a dynamic market model where buyers and sellers submit limit orders. If at a given moment in time, the buyer is unable to complete his entire order due to the shortage of sell orders at the required limit price, the unmatched part of the order is recorded in the order book. Subsequently these buy unmatched …
I show that the solution of a standard clearing model commonly used in contagion analyses for financial systems can be expressed as a specific form of a generalized Katz centrality measure under conditions that correspond to a system-wide shock. This result provides a formal explanation for earlier empirical results wh…