ERM performs well in feature learning with minimal feature maps.
problem Empirical risk minimization in feature learning with square loss.
method Asymptotic and non-asymptotic analysis of ERM performance.
result Excess risk quantiles of ERM match those of oracle procedure under certain conditions.
The recent empirical success of unsupervised cross-domain mapping algorithms, between two domains that share common characteristics, is not well-supported by theoretical justifications. This lacuna is especially troubling, given the clear ambiguity in such mappings. We work with adversarial training methods based on IP…
This study maps cycling risks and discomfort in Zurich, offering personalized route recommendations.
problem High cycling accidents and discomfort in Smart Cities.
method Geolocated bike accidents data, kernel density contours, weather, time, accident type and severity analysis.
result Empirical continuous spatial risk estimations and personalized route recommendations.
This study maps systemic risks in TradFi and DeFi, highlighting their interdependence.
problem Systemic risks in traditional and decentralized finance.
method Conceptual model and comparative analysis of TradFi and DeFi.
result Systemic risks in DeFi can affect TradFi and vice versa, creating a crosstagion effect.
The paper describes fitting submanifolds to data using Sussmann's orbit theorem.
problem Fitting an immersed submanifold to random samples.
method Uses Sussmann's orbit theorem to ensure submanifold fitting. Reconstruction involves encoding times and decoding via flows of vector fields.
result A high-probability bound on excess risk for the reconstruction error.
Inspired by recent ideas on how the analysis of complex financial risks can benefit from analogies with independent research areas, we propose an unorthodox framework for mapping microfinance credit risk---a major obstacle to the sustainability of lenders outreaching to the poor. Specifically, using the elements of net…
We introduce simple cost and risk proxy metrics that can be attached to Treasury issuance strategy to complement analysis of the resulting portfolio weighted-average maturity (WAM). These metrics are based on mapping issuance fractions to their long-term, asymptotic portfolio implications for cost and risk under mechan…
The paper provides risk bounds for learning many response functions using linear regression.
problem Learning many response functions from a single dataset.
method Ordinary least squares regression in a high-dimensional feature space.
result Convergence guarantees on worst-case excess prediction risk for infinite response functions with finite VC dimension.
Modeling bank leverage dynamics to understand systemic risk in financial markets.
problem Understanding systemic risk in financial markets triggered by bank leverage dynamics.
method Developed a dynamical model of bank leverage, analyzing coupled dynamics in isolated and interconnected bank models.
result Identified a procyclical feedback loop between asset prices and leverage, leading to chaotic dynamics.
Formulates Markov property for risk-sensitive dynamic optimisation.
problem Risk-sensitive dynamic optimisation problems in discrete time.
method Formulates probabilistic Markov property under dynamic risk framework.
result Property holds for standard risk measures and has multiple equivalent versions.
Optimal hedging framework with variational preferences under convex risk measures.
problem Optimal hedging with variational preferences under convex risk measures.
method Theoretical hedging optimization framework with dual representation of risk measures and utilities.
result Derivation of optimality and indifference pricing conditions.
One of the crucial problems in mathematical finance is to mitigate the risk of a financial position by setting up hedging positions of eligible financial securities. This leads to focusing on set-valued maps associating to any financial position the set of those eligible payoffs that reduce the risk of the position to …
Develops quantile diffusions for risk analysis in continuous time.
problem Stochastic dynamics of quantiles in continuous time.
method Construction of quantile processes through composite maps of distribution and quantile functions.
result Powerful method for interpreting quantile process characteristics in terms of model parameters.
We introduce a general framework for measuring risk in the context of Markov control processes with risk maps on general Borel spaces that generalize known concepts of risk measures in mathematical finance, operations research and behavioral economics. Within the framework, applying weighted norm spaces to incorporate …
Covariance shrinkage via stochastic interpolation
problem High-dimensional covariance estimation
method Recasting shrinkage as empirical risk minimization
result Reduces statistical risk through scheduling, flow maps, and early stopping
Framework for worst-case generation using Wasserstein space optimization.
problem Evaluating robustness and stress-testing systems under distribution shifts.
method Min-max optimization over continuous probability distributions in Wasserstein space.
result Global convergence guarantees for the proposed Gradient Descent Ascent scheme.
Introduces factor risk measures to assess risk relative to multiple factors.
problem Measuring risk relative to multiple factors.
method Introduces a double-argument mapping as a risk measure to assess risk relative to a vector of factors.
result Characterizes various types of factor risk measures including distortion, quantile, linear, and coherent measures.
New method for risk quantification using quantile processes and measure distortions.
problem Risk quantification and valuation in financial markets.
method Develops a novel stochastic valuation principle based on probability measure distortions induced by quantile processes.
result Introduces a system of subjective probability measures that indexes a stochastic valuation principle susceptible to probability measure distortions.
Set risk measures extend traditional risk measures to handle sets of positions.
problem Handling sets of positions with a single capital requirement.
method Developed an axiomatic framework for set risk measures, dual representation through topology and measures.
result Characterized worst-case set risk measures and provided examples.
Study characterizes training and test risks for MAP regression with Gaussian priors.
problem Understanding high-dimensional behavior of regularized linear regression with informative priors.
method Maximum a posteriori (MAP) regression with Gaussian priors, using random matrix theory.
result Closed-form risk formulas reveal the bias-variance-prior tradeoff and explain double descent.
Geospatial framework assesses climate risks for California's banking and exposed sectors.
problem Evaluating climate risks on banking and exposed sectors in California.
method Integrates hazard mapping, exposure analysis, and scenario-based financial risk assessment.
result Framework supports portfolio monitoring and institutional readiness under new standards.
Financial institutions have to allocate so-called "economic capital" in order to guarantee solvency to their clients and counter parties. Mathematically speaking, any methodology of allocating capital is a "risk measure", i.e. a function mapping random variables to the real numbers. Nowadays "value-at-risk", which is d…
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.
In the conditional setting we provide a complete duality between quasiconvex risk measures defined on L0 modules of the Lp type and the appropriate class of dual functions. This is based on a general result which extends the usual Penot-Volle representation for quasiconvex real valued maps.
Modeling financial systemic risk with optimal control theory for stability.
problem Analyzing and stabilizing systemic risk in interconnected financial entities.
method Developed a theoretical model using optimal control theory, including steps for synthesizing stabilizing controllers.
result The model ensures that the H∞ norms of the mappings from disturbance to output are less than a predefined constant, stabilizing the system. Develops Bayesian approach for end-to-end learning in stochastic optimization.
problem Stochastic optimization problems under uncertainty.
method Bayesian interpretation and new end-to-end learning algorithms.
result Improved decision maps for empirical risk minimization and distributionally robust optimization.
New guarantees for asymmetric sketching in compressive learning.
problem Statistical guarantees for compressive learning with asymmetric feature maps.
method Proves existing guarantees carry over to asymmetric scheme with LPD property, applies to quantized sketches.
result Existing statistical guarantees for compressive learning extend to asymmetric schemes with controlled error.
A new noise model for preferential Bayesian optimization using user anchors.
problem Inadequate assumption of homoscedastic noise in human-in-the-loop settings.
method Proposes a heteroscedastic noise model with anchors and a KDE uncertainty map.
result Risk-adjusted performance improvement and clarified anchor placement effects.
The present study deals with the analysis and mapping of Swiss franc interest rates. Interest rates depend on time and maturity, defining term structure of the interest rate curves (IRC). In the present study IRC are considered in a two-dimensional feature space - time and maturity. Geostatistical models and machine le…
Graph neural networks improve SME credit risk assessment.
problem Improving credit risk assessment for small and medium enterprises (SMEs).
method Graph neural networks were used to model the relationships between financial indicators of enterprises, creating a graph structure and embedding representations for credit risk prediction.
result The proposed model accurately predicts enterprise credit levels, demonstrating robustness and effectiveness.
Network science reveals corruption risk in EU procurement markets.
problem Identifying corruption risk in EU procurement markets.
method Analyzing a large dataset of public procurement contracts using network science.
result Corruption risk is clustered and varies by country, not just by market core or periphery.
Paper presents efficient IS for tail risk estimation with machine learning features.
problem Estimating Value at Risk and Conditional Value at Risk with black-box access.
method Efficient Importance Sampling algorithm with self-structuring transformation.
result Asymptotically optimal variance reduction in logarithmic scale.
New framework analyzes deep learning optimization with finite width networks, revealing generalization gaps and excess risks.
problem Analyzing generalization error of deep learning with finite width networks.
method Formulating neural network training as transportation map estimation and analyzing via infinite dimensional Langevin dynamics.
result Achieves fast learning rate and minimax optimal rates for classification and regression problems.
New method for efficient proximal mapping of 1-path-norm in shallow networks.
problem Efficiently handling the 1-path-norm of shallow neural networks.
method Closed-form proximal operator for efficient computation and upper bound on Lipschitz constant.
result Proximal mapping allows robust training against adversarial perturbations.
This paper maps the insurability of AI risks across various insurance products.
problem Emerging AI risks and their implications for insurance coverage.
method Coding 55 AI threat classes against 26 insurance products using public carrier materials and threat catalogs.
result Identification of a four-tier insurability frontier: affirmatively insured, silent-AI exposures, actively excluded, and unstructured perils.
The paper extends risk measures to two-step approximations and studies log-concave distributions.
problem Extending classical risk measures to two-step approximations.
method Optimization problem for determining optimal regime thresholds and values for log-concave distributions.
result Conditions for the uniqueness of regime changing in log-concave distributions.
New insights into risk aversion for complex decision models.
problem Understanding risk aversion in non-monotone decision models.
method Characterization of probabilistic risk aversion for generalized rank-dependent functions.
result Probabilistic risk aversion is determined by the distortion function, which is convex or scaled quantile-spread mixtures.
Optimizes risk assessment tools using mixed-integer programming.
problem Challenges in healthcare risk assessment due to label scarcity and asymmetric misclassification costs.
method Jointly optimizes scoring weights and category thresholds via mixed-integer programming (MIP).
result Prevents label-scarce category collapse and achieves more accurate risk categorization.
This paper studies a valuation framework for financial contracts subject to reference and counterparty default risks with collateralization requirement. We propose a fixed point approach to analyze the mark-to-market contract value with counterparty risk provision, and show that it is a unique bounded and continuous fi…
A new method finds diverse near-optimal portfolios using quality-diversity.
problem Optimizing financial portfolios with robustness to input parameter uncertainties.
method Quality-Diversity (QD) optimization using CVT-MAP-Elites algorithm.
result Diverse set of near-optimal portfolios identified.
Develops a framework for quantifying agentic AI model risk using LLM-inferred Bayesian state filters.
problem Quantifying the risk of agentic AI systems due to uncertain beliefs and actions.
method Representing the system as a partially observed Markov decision process with latent states, Bayesian belief updates, control-dependent losses, and tail-risk functionals.
result Develops a rigorous framework for separating uncertainty quantification from risk measurement.
Dynamic risk measures follow law invariance principles over time.
problem Tackles dynamic risk measurement principles.
method Shows equivalence between adapted law invariance and recursive one-step conditional-law representation for time-consistent risk measures.
result Identifies adapted law invariance as the dynamic counterpart of ordinary law invariance.
The paper develops a theory for one-step Wasserstein-guided models for PDE-induced measures.
problem Theoretical understanding of generative models' accuracy in scientific computing.
method Regularity theory for optimal transport between doubling measures, excess-risk bounds.
result One-step Wasserstein-guided generative models can approximate PDE-induced measures with Hölder continuity.
A new framework for brain mapping using statistical agnostic methods.
problem Estimating brain connectivity with limited data and controlling false positives.
method Statistical Agnostic Mapping (SAM) based on concentration inequalities.
result Relieves instability and provides less conservative p-value correction.
This study uses TDA to map corporate failure, revealing distinct regions of risk.
problem Understanding and predicting corporate default risk.
method Topological Data Analysis (TDA) applied to Altman's Z-score model.
result Firms do not cluster neatly along default predictors, suggesting complex risk landscapes.
This paper discusses the role of risk communication in macroprudential oversight and of visualization in risk communication. Beyond the soar in data availability and precision, the transition from firm-centric to system-wide supervision imposes vast data needs. Moreover, except for internal communication as in any orga…
Modeling bank leverage dynamics using dynamical systems and neural networks.
problem Understanding leverage dynamics in financial systems.
method Dynamical systems, deep neural networks, adaptive expectation scheme.
result Chaotic behavior in leverage dynamics for a significant fraction of banks.
A new framework assesses liquidity risk in perpetual futures exchanges.
problem Measuring and predicting liquidation execution risk in perpetual futures markets.
method Slippage-at-Risk (SaR) framework, comprising three metrics: cross-sectional slippage quantile, expected slippage, and aggregate dollar-denominated tail slippage.
result SaR provides a forward-looking assessment of liquidation execution risk, predictive of systemic stress.