Maps obstructing positive scalar curvature and inessentialness.
problem Obstructing metrics with positive scalar curvature and inessential submanifolds.
method Construction of wrong way maps in uniformly finite homology and homology of groups.
result Obstructions to positive scalar curvature metrics and inessential submanifolds.
Study normal bundle and deformation to get new pushforward maps.
problem Construct pushforward maps in various homology theories.
method Use deformation Lie groupoids to construct pushforward maps.
result Functoriality of pushforward maps recovers and generalizes previous cases.
Proposes a new framework for environmental CVA with robust wrong-way risk.
problem Limited operational implementations of translating environmental scenarios into CVA.
method Three components: hazard rate mapping, tail generators, and KL divergence-based wrong-way risk bound.
result Nature CVAs can vary significantly across different ecosystem generators.
For a Lie groupoid G with a twisting (a PU(H)-principal bundle over G), we use the (geometric) deformation quantization techniques supplied by Connes tangent groupoids to define an analytic index morphism in twisted K-theory. In the case the twisting is trivial we recover the analytic index morphism of the groupoid. Fo…
The study highlights the importance of Wrong-Way Risk in FVA calculations during financial market turmoil.
problem The relevance of Wrong-Way Risk in Funding Valuation Adjustments (FVA) during financial market uncertainty.
method The study examines the impact of various modelling choices, including default times and stochastic/deterministic funding spreads, on FVA calculations.
result WWR effects are non-negligible in FVA modelling from a risk-management perspective.
A new method uses liquid options to hedge and price wrong way risk in credit valuation adjustment.
problem Managing wrong way risk (WWR) for CVA, specifically in credit valuation adjustment (CVA).
method Model-free worst-case approach based on static hedging of counterparty exposure with liquid options.
result Option-based hedges significantly reduce practical WW-CVA, making it more realistic and practical.
Wrong-way risk in counterparty and funding exposures is most dramatic in the situations of systemic crises and tails events. A consistent model of wrong-way risk (WWR) is developed here with the probability-weighted addition of tail events to the calculation of credit valuation and funding valuation adjustments (CVA an…
Model assesses risks in CCP networks, identifying wrong-way risks.
problem Credit and liquidity risks in CCP networks.
method Developed a model to capture features of gap risk, feedback, and different participant risks.
result Identified wrong-way risks between clearing member defaults and market turbulence.
Proposes a new method to assess Wrong-Way Risk in cross-currency swaps.
problem Addressing Wrong-Way Risk (WWR) in cross-currency swaps with stochastic correlation modeling.
method Proposes a stochastic correlation approach to model the dependency between exposure and counterparty credit risk, capturing tail dependence.
result The impact of stochastic correlation on calculated CVA is substantial, providing a promising method to model WWR.
Efficiently models Wrong-Way Risk in FVA without full Monte Carlo.
problem Assessing Wrong-Way Risk in Funding Valuation Adjustments (FVA) without extensive simulations.
method Splitting exposure into independent and WWR-driven parts; approximating WWR-driven part using Gaussian stochastic factor.
result An efficient and robust method to include WWR in FVA modelling.
Paper compares analytical and dynamic approaches for wrong-way risk modeling in finance.
problem Modeling wrong-way risk in financial contracts like CVA.
method Static and dynamic approaches, including a new dynamic approach using survival process.
result Analytical derivation of positive exposures and expected values in dynamic models.
New method to price CVA by adjusting exposure drift to eliminate Wrong-Way Risk.
problem Addressing Wrong-Way Risk (WWR) in Credit Value Adjustment (CVA) pricing.
method Stochastic intensity approach with changes of measure to embed WWR in exposure drift.
result Elimination of WWR explicitly in pricing problem, leading to tractable approximation.
Abstract machinery finds obstructions to uniform positive scalar curvature.
problem Finding obstructions to uniform positive scalar curvature.
method Coarse index theory and embedding submanifolds.
result Abstract machinery constructs wrong way maps on K-theory. The construction of topological index maps for equivariant families of Dirac operators requires factoring a general smooth map through maps of a very simple type: zero sections of vector bundles, open embeddings, and vector bundle projections. Roughly speaking, a normally non-singular map is a map together with such a …
A new model reduces Wrong-Way Risk in CVA pricing.
problem Limiting Wrong-Way Risk (WWR) in CVA pricing models.
method Subordinated Cox-Ingersoll-Ross (CIR) intensity model with time-changing intensities.
result The new model introduces significant WWR compared to JCIR++.
Paper calculates robust FVA for OTC derivatives under distributional uncertainty.
problem Distributional uncertainty in over the counter derivatives valuation.
method Wasserstein distance as ambiguity measure, dual formulation of robust FVA optimization.
result Additional FVA charge due to distributional uncertainty measured under various configurations.
Paper calculates robust XVA for derivatives under distributional uncertainty using Wasserstein distance.
problem Distributional uncertainty in over-the-counter derivatives pricing.
method Wasserstein distance as ambiguity measure, dual formulations derived using Lagrangian duality.
result Characterization and quantification of wrong-way counterparty credit and funding risks.
Analyzes valuation of derivative claims with asymmetric funding costs and WWR.
problem Valuing and hedging derivative claims with bilateral cash flows in asymmetric funding and risk environments.
method Characterizes pre-default claim value as solution to a non-linear Cauchy problem, applies stochastic representation under linear funding policy.
result Derivative claim value can be represented as a portfolio of European options and admits an analytical formula involving elementary functions and Gaussian integrals.
The dynamic Gaussian copula model shows default times are invariant, contrary to the immersion property.
problem The dynamic Gaussian copula model's default times exhibit unexpected invariance properties.
method Proof of invariance properties of default times in the dynamic Gaussian copula model.
result Default times in the dynamic Gaussian copula model are invariant, contrary to the immersion property.
Approximates CVA of European options with WWR using correlation expansions.
problem Computing CVA of European options with Wrong Way Risk in a default intensity setting.
method Exploits a correlation expansion approach to approximate option pricing.
result Numerical evaluations show the method's performance compared to existing methods.
The study corrects misconceptions in GBDT speed benchmarks.
problem Misleading speed benchmarks of GBDT algorithms.
method Explained and criticized several straightforward benchmarking methods, outlined fair benchmark requirements.
result A fair GBDT speed benchmark requires specific conditions.
Causal Set Theory's Hauptvermutung is resolved in two ways, one of which is true.
problem Formulating and resolving the Hauptvermutung in Causal Set Theory.
method Two mathematically well-defined formulations of the Hauptvermutung, one of which is true.
result The Hauptvermutung is true when finite sets are replaced by countable sets.
Solves worst-case joint distribution problem for financial risk factors.
problem Finding worst-case joint distribution of risk factors given marginals and loss function.
method Uses linear programming to solve the problem when CVaR is the risk measure and distributions are discretized.
result Demonstrates method's applicability to various financial contexts, including counterparty credit risk.
This paper examines limitations of machine learning models in social systems.
problem Understanding and addressing the shortcomings of machine learning models in social applications.
method Structured overview of conceptual, procedural, and statistical limitations.
result Identification of failure points and ways to address them.
The introduction of CCPs in most derivative transactions will dramatically change the landscape of derivatives pricing, hedging and risk management, and, according to the TABB group, will lead to an overall liquidity impact about 2 USD trillions. In this article we develop for the first time a comprehensive approach fo…
The paper analyzes credit valuation adjustments under collateralized interest rate derivatives, introducing a new dynamics for multiple interest rate curves.
problem The impact of multiple interest rate curves on credit valuation adjustments under collateralized models.
method Formulated a consistent dynamics for multiple interest rate curves, including the margin period of risk and stochastic basis for wrong-way risk analysis.
result Numerical results confirm the importance of stochastic basis for proper wrong-way risk analysis of sensitive products like basis swaps.
Geometrically describes homology of surface bundles over surfaces.
problem Understanding the homology of surface bundles over surfaces.
method Geometric description using holonomy map.
result Observations on the homology of surface bundles, replacing a previous theorem.
Study shows how to better estimate credit provisions and economic capital.
problem Estimating credit provisions and economic capital accurately.
method Using supermodularity ordering properties and elliptically distributed latent factors.
result Convex risk measures of credit losses are nondecreasing w.r.t. various covariances.
The paper defines K-theoretic secondary invariants for Lie groupoids and proves related index theorems.
problem Constructing secondary invariants for Lie groupoids and proving their properties.
method Lie groupoid version of constructions from Piazza and Schick, focusing on adiabatic deformations and geometric operators.
result Lie groupoid version of Delocalized APS Index Theorem and product formula for secondary invariants.
Combining interpretability and stability methods improves DNN robustness.
problem Improving interpretability and robustness of deep neural networks.
method Combining interpretability (conductance) and stability (binary classifier) methods to detect and discard wrong predictions.
result Combining interpretability and stability methods increases model robustness.
Defines and computes geometric pairings for discrete groups using Baum-Connes assembly map.
problem Defining and computing geometric pairings for discrete countable groups.
method Constructs explicit morphisms and the Chern-Baum-Connes assembly map.
result Explicit formulation of a Chern-Connes pairing with the periodic cyclic cohomology of the group algebra.
Paper proposes a method to detect adversarial examples using saliency.
problem Detecting adversarial perturbations in machine learning models.
method Trains a binary classifier with origin data and saliency data.
result Shows good performance in detecting adversarial perturbations.
A graph's winding numbers around two non-adjacent vertices differ by ±1.
problem Understanding the winding numbers of a specific graph configuration in the plane.
method Analyzing continuous maps from a graph to the plane, focusing on the winding numbers of specific cycles.
result The difference in winding numbers of a cycle around two non-adjacent vertices is ±1.
Counterparty Risk FAQ: Credit VaR, PFE, CVA, DVA, Closeout, Netting, Collateral, Re-hypothecation, WWR, Basel, Funding, CCDS and Margin Lendingq-fin.PR We present a dialogue on Counterparty Credit Risk touching on Credit Value at Risk (Credit VaR), Potential Future Exposure (PFE), Expected Exposure (EE), Expected Positive Exposure (EPE), Credit Valuation Adjustment (CVA), Debit Valuation Adjustment (DVA), DVA Hedging, Closeout conventions, Netting clauses, Collateral …
The paper shows DR maps can't be perfect in information retrieval.
problem The limitations of DR maps in achieving perfect precision and recall.
method Quantitative topology approach, proving precision bounds, introducing Wasserstein distance.
result Continuous DR maps must have imperfect precision, and a new precision measure based on Wasserstein distance is proposed.
Everyone misunderstands the Sharpe ratio, which measures risk in finance.
problem Misunderstanding of the Sharpe ratio as a risk metric.
method A critical analysis and rectification of the Sharpe ratio concept.
result Clarification of the Sharpe ratio's role in risk assessment.
The market practice of extrapolating different term structures from different instruments lacks a rigorous justification in terms of cash flows structure and market observables. In this paper, we integrate our previous consistent theory for pricing under credit, collateral and funding risks into term structure modellin…
This paper addresses recalibration issues in hedging callable assets, proposing a new risk-adjusted approach.
problem The mismatch between dynamic hedging theory and practice due to daily recalibration.
method Extends HVA model risk approach to callable assets, focusing on recalibration and model risks.
result Model risk reserves adjusted for exercise decisions may significantly exceed basic valuation differences.
A new update rule for deep reinforcement learning reduces learning variance and variance in reference signals.
problem Learning variance and incorrect reference signals in deep reinforcement learning.
method t-soft update method inspired by student-t distribution, which reduces extreme updates and accelerates similar updates.
result The t-soft update method outperforms conventional methods in terms of return and variance in PyBullet robotics simulations.
Proposes m-POT to improve m-OT's misspecified mappings issue.
problem Misspecified mappings in mini-batch optimal transport.
method Partial optimal transport (POT) between mini-batch empirical measures.
result m-POT alleviates incorrect mappings compared to current methods.
Improved the convergence proof of ADAM-Optimizer.
problem Incorrect convergence proof of ADAM-Optimizer.
method Provided an improved convergence proof.
result Corrected the convergence proof of ADAM-Optimizer.
The book examines statistical issues with fat-tailed distributions and proposes remedies.
problem Misapplication of conventional statistical techniques to fat-tailed distributions.
method Investigates the limitations of traditional asymptotics and proposes remedies.
result Traditional statistical techniques often fail when applied to fat-tailed distributions.
Neural networks can predict BMI from faces, and can be fooled into wrong predictions.
problem Vulnerability of BMI prediction models to adversarial attacks.
method Test-time adversarial attacks on neural networks trained to infer BMI from facial images.
result Neural networks can be tricked into predicting incorrect BMI values, posing a risk of insurance fraud.
A geometric theory explains loss functions for robust representation learning.
problem Treats robustness, domain adaptation, and sensor drift as separate literatures.
method Estimates covariance Sigma_task and uses it to pin Jacobian penalties.
result Proves optimality and necessity of range coverage for penalty matrices.
Framework learns interpretable concepts from data without interventions.
problem Learning spurious correlations between concepts in CBMs.
method Causal representation learning (CRL) to align latent variables with interpretable concepts using few labels.
result Framework provides theoretical guarantees on correctness and number of required labels without interventions.
Unsupervised learning models can produce accurate but misleading predictions.
problem Widespread misleading predictions in unsupervised learning models.
method Developed Explainable AI techniques to detect misleading predictions.
result Widespread Clever Hans effects in unsupervised learning models.
Pixle attacks images by rearranging pixels, bypassing neural networks.
problem Vulnerability of neural networks to black-box adversarial attacks.
method A novel attack that rearranges a small number of pixels in images.
result Successfully attacks a high percentage of samples on various datasets and models.
Unified study of harmonic maps between pseudo-Riemannian surfaces.
problem Classifying harmonic maps between pseudo-Riemannian surfaces.
method Unified formalism and Bäcklund transformation.
result Unified solutions to harmonic map equations and corresponding maps.