We quantify the sensitivity of the Eisenberg-Noe clearing vector to estimation errors in the bilateral liabilities of a financial system in a stylized setting. The interbank liabilities matrix is a crucial input to the computation of the clearing vector. However, in practice central bankers and regulators must often es…
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48 results for “clearing vectors”
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.
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.
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…
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.
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 -graded manifolds theory. We introduce -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…
Systemic Risks in CCP Networksq-fin.MF
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.
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.
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.
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 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.
Yang-Mills Meets Datamath.DG
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.
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.
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.
Recent innovations in Information and Communication Technologies (ICT) provide new opportunities and challenges for integration of distributed energy resources (DERs) into the energy supply system as active market players. By increasing integration of DERs, novel market platform should be designed for these new market …
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.
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.
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 .
Improved Hardness Results for the Clearing Problem in Financial Networks with Credit Default Swapscs.GT
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.
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…
The call auction is a widely used trading mechanism, especially during the opening and closing periods of financial markets. In this paper, we study a standard call auction problem where orders are submitted according to Poisson processes, with random prices distributed according to a general distribution, and may be c…
Sequential processing biases asset allocation in artificial stock markets.
problem Systematic bias in asset allocation due to sequential processing of order books.
method Examined the impact of sequential versus parallel clearing mechanisms on multi-asset price dynamics.
result Sequential processing introduces a significant bias affecting the allocation of traders' capital.
This paper optimizes portfolio compression by reducing excess notional in market contracts.
problem Reduction of excess notional in market contracts to decrease systemic risk.
method Examines and solves portfolio compression problems using graph theory and algorithms.
result Developed a clearing algorithm and method to compute maximum volume conservative compression.
Einstein's non-symmetric geometry uses Bochner's technique to prove decomposition and vanishing results.
problem Analyzing Einstein's non-symmetric geometry with Bochner's technique.
method Defining concepts, proving decomposition formula, and showing vanishing results.
result Vanishing results about the null space of Bochner and Hodge type Laplacians.
In implicit models, one often interpolates between sampled points in latent space. As we show in this paper, care needs to be taken to match-up the distributional assumptions on code vectors with the geometry of the interpolating paths. Otherwise, typical assumptions about the quality and semantics of in-between points…
Paper analyzes fire sales in a network of banks using VWAP and LOB pricing.
problem Optimal asset liquidation and borrowing strategies in a network of banks.
method Nash equilibrium model with two market clearing mechanisms.
result Existence and uniqueness of clearing solutions for liquidations, borrowing, prices, and haircuts.
This study analyzes costs of CCP default resolution using Radner equilibrium approach.
problem Analyzing costs of CCP default resolution for investment banks' derivatives.
method Radner equilibrium approach for portfolio allocation and price discovery.
result Radner equilibria uniquely exist and provide solutions for market equilibria.
A new method for sparse regression models using graph structure.
problem Sparse regression models for high-dimensional data.
method Decomposes coefficient vector into latent variables, performs regularization on latent variables, uses proximal projection.
result Stable performance compared to other models, especially for high-dimensional data.
We present an approach to Jacobi and contact geometry that makes many facts, presented in the literature in an overcomplicated way, much more natural and clear. The key concepts are Kirillov manifolds and linear Kirillov structures, i.e., homogeneous Poisson manifolds and, respectively, homogeneous linear Poisson manif…
Central Counterparty Riskq-fin.RM
A clearing member of a Central Counterparty (CCP) is exposed to losses on their default fund and initial margin contributions. Such losses can be incurred whenever the CCP has insufficient funds to unwind the portfolio of a defaulting clearing member. This does not necessarily require the default of the CCP itself. In …
Tax systems ensure sustainable economic development by adjusting production technologies and gross output volumes.
problem Ensuring sustainable economic development through optimal tax systems.
method Explicit formulas and mathematical proofs for tax systems based on production technologies and gross output volumes.
result The vector of gross output must belong to the interior of the cone formed by the columns of the total cost matrix under perfect taxation systems.
This paper provides a framework for modeling the financial system with multiple illiquid assets during a crisis. This work generalizes the paper by Amini, Filipovic and Minca (2016) by allowing for differing liquidation strategies. The main result is a proof of sufficient conditions for the existence of an equilibrium …
BERET improves binary expansion test for multivariate independence.
problem Testing independence of random vectors in arbitrary dimensions.
method Ensemble approach using sum of squared symmetry statistics and distance correlation.
result Improves power while preserving interpretability.