The paper identifies and critiques problems with risk matrices using ordinal scales.
problem Problems with risk matrices using ordinal scales.
method Overview of risk assessment process, explanation of fallacies, and suggestions for improvement.
result The paper proposes avoiding risk matrices and using fully quantitative methods instead.
Study calculates tail risk for various mixture distributions.
problem Estimating tail risk for complex distribution mixtures.
method Analyzes tail conditional expectation for location-scale mixtures of elliptical distributions.
result Developed methods for calculating tail risk in various distributions.
This paper presents a novel scaling method for unbiased risk estimation.
problem Challenges in risk assessment due to limited data, non-stationarity, and heavy tails.
method Develops a statistical framework for efficient risk scaling, extending beyond the square-root-of-time rule.
result Ensures robust and conservative risk estimation, applicable to small sample settings.
Proposes a new tail risk measure based on the most probable maximum risk event size.
problem Current risk measures like VaR and ES are limited in their applicability and require specifying a confidence level.
method Develops a new risk measure called MPMR that does not require a confidence level and scales with the length of the time interval.
result The new risk measure, MPMR, scales with the number of observations by a power law, allowing for reliable estimations of long-term risks based on short-term estimations.
High-dimensional shrinkage risk depends on the default prior for the common scale.
problem Choosing the default prior for the common scale in high-dimensional shrinkage.
method Using radial-power benchmark to compare variance-flat and standard deviation-flat priors.
result The standard deviation-flat prior has a one-unit asymptotic risk advantage near the origin.
This thesis examines the accuracy of scaling VaR estimates for longer holding periods.
problem The accuracy of VaR estimates for longer holding periods using the square root of time rule.
method Examined VaR scaling for longer holding periods using empirical analysis.
result Scaling can provide good estimates of VaR but may lead to significant losses over time.
In this paper we discuss a general methodology to compute the market risk measure over long time horizons and at extreme percentiles, which are the typical conditions needed for estimating Economic Capital. The proposed approach extends the usual market-risk measure, ie, Value-at-Risk (VaR) at a short-term horizon and …
Novel framework for systemic risk analysis in financial markets.
problem Systemic risk in financial markets.
method Multi-scale network dynamics, transfer entropy networks, agent-based modeling, wavelet decomposition, Model Context Protocol (MCP).
result Multi-scale approach reveals hidden systemic risk patterns.
Paper presents an efficient algorithm for learning minimax risk classifiers with large-scale data.
problem Efficient learning of minimax risk classifiers for large-scale data with multiple classes.
method Combination of constraint and column generation for efficient learning.
result 10x speedup for general large-scale data and 100x speedup with many classes.
New method calibrates noise for attack risk, improving ML model accuracy.
problem Improving accuracy of privacy-preserving ML models while maintaining privacy.
method Directly calibrates noise scale to a desired attack risk level, bypassing the standard ε-calibration. result Significantly decreases noise scale, leading to increased utility at the same risk level.
The paper uses EVT to improve tail risk measures under ambiguity sets.
problem Misspecification of tail risk measures leads to inflated risk estimates.
method Applies Extreme Value Theory to derive worst-case tail risk under ambiguity sets.
result Proposes a tail-calibrated ambiguity design that preserves nominal tail asymptotic scaling.
Modeling risk and performance with Levy-stable distributions.
problem Understanding risk and performance in financial markets with non-Gaussian distributions.
method Developed a finite-horizon model using Levy-stable scaling, identified parameters from data, derived formulas for various financial ratios.
result Horizon-correct formulas for risk measures are derived and validated across different horizons.
Simple policy outperforms complex ones in cloud auto-scaling.
problem Predicting resource scaling for large-scale cloud applications with limited deployment throughput.
method Probabilistic workload forecast for auto-scaling decisions based on risk aversion.
result The proposed policy outperforms sophisticated and simple benchmark policies in real-world and synthetic data.
New algorithms optimize risk for large datasets, improving efficiency.
problem Optimizing risk for large datasets with robust methods.
method Proposed algorithms for distributionally robust optimization with CVaR and χ² divergence uncertainty sets.
result Algorithms require independent gradient evaluations of training set size and parameters, suitable for large-scale applications.
This paper investigates the hedging effectiveness of a dynamic moving window OLS hedging model, formed using wavelet decomposed time-series. The wavelet transform is applied to calculate the appropriate dynamic minimum-variance hedge ratio for various hedging horizons for a number of assets. The effectiveness of the dy…
New approach improves classification guarantees by focusing on direction rather than regression risk.
problem Improving classification guarantees in binary classification problems.
method Establishing a geometric distinction between classification and regression, leveraging scale invariance.
result Improved guarantees for classification risk compared to regression risk.
Paper compares ML methods for credit scoring, highlighting feature selection and scaling impacts.
problem Determining default risk in credit scoring models.
method Eight ML methods (SVM, Naive Bayes, DT, RF, XGBoost, KNN, MLP, LR) with feature selection and scaling.
result Feature selection and scaling improve model performance in credit scoring.
Temperature scaling fails for distributions with class overlaps, while Mixup improves calibration.
problem Temperature scaling's performance degrades with class overlaps, leading to poor calibration.
method Identified temperature scaling's limitations and compared it with Mixup for calibration.
result Mixup significantly outperforms temperature scaling in calibration metrics with class overlaps.
The paper introduces a new method for forecasting financial risk using quantile-based modeling.
problem Forecasting Value-at-Risk (VaR) and Expected Shortfall (ES) for financial returns.
method Semiparametric approach using restricted quantile regression to model the conditional scale of financial returns.
result The method provides robust, distribution-free estimates of extreme losses and captures risk dynamics.
Paper addresses theoretical risks in neural MCCFR, proposing Robust Deep MCCFR for improved performance.
problem Theoretical risks in neural MCCFR, especially in large games.
method Adaptive framework with selective component deployment, including target networks, exploration, and variance-aware training.
result Robust Deep MCCFR achieves significant exploitability improvements in both Kuhn and Leduc Poker.
Paper assesses risks of stablecoins, from lending to business-to-business.
problem Credit risks in decentralized stablecoin issuance.
method Examines mechanisms, risks, and mitigation strategies at each layer.
result Potential for scaling stablecoins while maintaining systemic health.
The paper analyzes Indian stock sectors using multifractal analysis for long and short-term investment.
problem Investment risk and stability in Indian stock sectors.
method Sector-wise multifractal analysis of Bombay Stock Exchange, India, over short and long time scales.
result Long-term investment in stable sectors is more profitable, while sectors with large fluctuations may lead to downturns.
In stochastic optimization, the population risk is generally approximated by the empirical risk. However, in the large-scale setting, minimization of the empirical risk may be computationally restrictive. In this paper, we design an efficient algorithm to approximate the population risk minimizer in generalized linear …
This paper reviews the economic and theoretical foundations of insolvency risk measurement and capital adequacy rules. The proposed new measure of insolvency risk is constructed by disentangling assets, debt and equity at the micro-prudential firm level. This new risk index is the Firm Insolvency Risk Index (FIRI) whic…
Improved model accuracy can reduce overall user accuracy in competitive markets.
problem The impact of model competition on overall user accuracy.
method Defined a model of competition for classification tasks and used data representations to study the effect of scale.
result Improving data representation quality can decrease overall predictive accuracy across users (social welfare) in a competitive market.
Paper introduces robust kernel ridge regression using Cauchy loss for handling various noise types.
problem Developing robust regression methods for noisy data.
method Introduces kernel Cauchy ridge regressor (KCRR) using Cauchy loss function.
result Establishes almost minimax-optimal convergence rate for KCRR in terms of L2-risk. SignSGD outperforms SGD in linear regression with optimal scaling laws under PLRF model.
problem Improving linear regression performance with signSGD under power-law random features.
method Analysis of signSGD risk under PLRF model, comparison with SGD, identification of unique effects.
result SignSGD can have a steeper compute-optimal slope than SGD in noisy regimes, especially with WSD schedule.
Proposes a new framework for learning image augmentations to improve classification performance.
problem Improving classification performance with a given class of predictors.
method Transformed Risk Minimization (TRM) framework that optimizes both predictive models and data transformations.
result Performance of TRM with SCALE algorithm compares favorably to prior methods on CIFAR10/100.
This article develops the theory of risk budgeting portfolios, when we would like to impose weight constraints. It appears that the mathematical problem is more complex than the traditional risk budgeting problem. The formulation of the optimization program is particularly critical in order to determine the right risk …
The paper extends entropy maximization to multiscale settings and applies it to neural networks.
problem Achieving optimal risk bounds in neural networks using multiscale entropy.
method Generalizing maximum entropy to multiscale settings and applying it to neural networks.
result The multiscale Gibbs posterior can achieve a smaller excess risk than the single-scale Gibbs posterior in a teacher-student scenario.
This work explains scaling laws as redundancy laws in deep learning.
problem The mathematical origins of scaling laws in deep learning models remain unclear.
method Kernel regression and analysis of data covariance spectra.
result Scaling laws can be explained as redundancy laws, revealing the learning curve's slope depends on data redundancy.
Ensembles of random-feature models can't outperform a single large model.
problem Finding the optimal balance between model size and ensemble size.
method Deterministic equivalent risk estimates and scaling laws analysis.
result Ensembles of random-feature models achieve near-optimal performance only under specific conditions.
ADGAN improves risk tolerance prediction by aligning cross-domain data.
problem Lack of professional knowledge and domain-specific models in risk tolerance studies.
method Asymmetric cross-Domain Generative Adversarial Network (ADGAN) for domain scale inequality.
result ADGAN better handles class imbalance and unqualified data than state-of-the-art methods.
Scaling and multiscaling financial time series have been widely studied in the literature. The research on this topic is vast and still flourishing. One way to analyze the scaling properties of time series is through the estimation of their scaling exponents, that are recognized as being valuable measures to discrimina…
Develops a new method for risk diversification using dynamic risk measures.
problem Dynamic risk diversification in investment portfolios.
method Introduces dynamic risk contributions and a recursive optimization approach for coherent dynamic distortion risk measures.
result Dynamic risk budgeting strategies can be solved using deep learning.
New method estimates model risk without knowing function class.
problem Evaluating model risk for complex, opaque models.
method Wild refitting with Bregman losses and randomized symmetrization.
result Valid upper bound on excess risk for opaque models.
Quantum reservoirs risk bounds are analyzed using Rademacher complexity.
problem Bounding generalization errors of quantum reservoirs.
method Using Rademacher complexity, specific bounds are derived for quantum reservoir classes.
result Risk bounds converge with increasing training samples and qubits.
Gradient descent performs well on weakly convex losses, offering generalization guarantees.
problem Learning with weakly convex losses using gradient descent.
method Analyzing the stability of gradient descent through the smallest eigenvalue of the Hessian.
result Generalization error bounds hold under a wider range of step sizes.
This paper improves traditional Markowitz optimization by considering variance at multiple time scales.
problem Traditional Markowitz optimization limits to a single time scale, ignoring variance across different frequencies.
method Introduces multifrequency optimization allowing specification of target Hurst exponents across multiple time scales.
result Effective risk management strategy that aligns with investor preferences at various time scales.
Study dynamic risk measures with distributional uncertainty using optimal transport.
problem Risk robustification under distributional uncertainty in Markovian models.
method Characterize risk measures via convex monotone semigroups and optimal transport costs.
result Identify generator and correction terms for dynamic risk measures under different scaling regimes.
In high-stakes machine learning applications, it is crucial to not only perform well on average, but also when restricted to difficult examples. To address this, we consider the problem of training models in a risk-averse manner. We propose an adaptive sampling algorithm for stochastically optimizing the Conditional Va…
This thesis presents the Conditional Value-at-Risk concept and combines an analysis that covers its application as a risk measure and as a vector norm. For both areas of application the theory is revised in detail and examples are given to show how to apply the concept in practice. In the first part, CVaR as a risk mea…
Power-law portfolios improve diversification by scaling weights sub-linearly.
problem Optimization methods struggle with unstable pair correlations and non-Gaussian risk measures.
method Construct portfolios with penalty proportional to arbitrary order moment of returns, leading to sub-linear weight scaling.
result Infinite order power-law portfolios are perfectly diversified, improving diversification over Kelly portfolios.
We investigate the ergodic problem of growth-rate maximization under a class of risk constraints in the context of incomplete, Itô-process models of financial markets with random ergodic coefficients. Including {\em value-at-risk} (VaR), {\em tail-value-at-risk} (TVaR), and {\em limited expected loss} (LEL), these cons…
Interpolating models can have heavy-tailed risk, leading to rare but severe errors.
problem Interpolating models' tail risk is poorly understood, affecting rare but impactful errors.
method Large-deviation methods to study the fragility of high-dimensional linear interpolators.
result Ridgeless regression exhibits heavy-tailed risk, while ridge-regularized estimators have better tail behavior.
We perform a large-scale simulation of an Ising-based financial market model that includes 300 asset time series. The financial system simulated by the model shows a fat-tailed return distribution and volatility clustering and exhibits unstable periods indicated by the volatility index measured as the average of absolu…
Implementing large-scale information and communication technology (IT) projects carries large risks and easily might disrupt operations, waste taxpayers' money, and create negative publicity. Because of the high risks it is important that government leaders manage the attendant risks. We analysed a sample of 1,355 publ…
The entropic value-at-risk (EVaR) is a new coherent risk measure, which is an upper bound for both the value-at-risk (VaR) and conditional value-at-risk (CVaR). As important properties, the EVaR is strongly monotone over its domain and strictly monotone over a broad sub-domain including all continuous distributions, wh…