The paper optimizes portfolios using a new GARCH model with regime switching and tempered stable innovations.
problem Mitigating left tail risk in multi-asset portfolios.
method Proposes a Markov regime-switching GARCH model with multivariate normal tempered stable innovation (MRS-MNTS-GARCH) for portfolio optimization.
result Optimal portfolios with tail risk measures outperform standard deviation-based portfolios and equally weighted portfolios in various performance metrics.
Paper provides tail bounds for stochastic mirror descent in heavy-tailed noise.
problem Optimizing convex and Lipschitz functions with heavy-tailed noise.
method Develops tail bounds for optimization error of Stochastic Mirror Descent.
result Tail bounds extend to heavier-tailed noise regimes without diameter constraints.
New theory predicts deep neural networks can operate in an extended critical regime without fine-tuning.
problem Understanding the dynamics and computational principles of deep neural networks.
method Combining theories of heavy-tailed random matrices and non-equilibrium statistical physics.
result Deep neural networks can operate in an extended critical regime without fine-tuning parameters.
Proposes a tail-adaptive shrinkage method for robust sparse estimation.
problem Robust Bayesian methods for high-dimensional regression under diverse sparse regimes.
method Global-local-tail (GLT) Gaussian mixture distribution with tail-adaptive shrinkage.
result GLT posterior contracts at minimax optimal rate for sparse normal mean models.
The standard deviation and Gini mean difference order based on tail behavior.
problem Ordering between standard deviation and Gini mean difference for real-valued risks.
method Analysis of the mean excess function of the pairwise difference ∣X−X′∣. result Dominance regimes of SD and GMD are determined by tail behavior of the distribution.
Is AdamW effective under heavy-tailed noise?
problem Stochastic gradient noise in LLM pretraining is typically heavy-tailed.
method Formulate as an open problem, prove a positive weighted-metric benchmark, and give a corridor lower-bound mechanism.
result No rigorous convergence theory for AdamW established in heavy-tailed regime.
Model predicts global financial market risks and asset allocation.
problem Predicting downside risk and market regime shifts.
method Dynamic regime switching model based on GARCH-DCC-Copula.
result Significantly improves risk and alpha-based asset allocation strategies.
Bayesian VAR and Elliptical Black-Litterman models improve portfolio optimization during regime changes and heavy-tailed returns.
problem Portfolio optimization under market regime changes and heavy-tailed returns.
method BAVAR-BLED algorithm combining BAVAR and Black-Litterman models with Elliptical Distributions.
result Significant outperformance of state-of-the-art methods in Sharpe, Sortino ratios, and total returns.
New framework estimates treatment effects in extreme data.
problem Hindered by unavailability of counterfactual outcomes and rarity of extreme data.
method Proposes a new framework based on extreme value theory.
result Quantifies treatment effects using tail decay rates of potential outcomes.
Exact tail probability bounds for bounded kurtosis.
problem Determining worst-case tail probabilities under kurtosis constraints.
method AI-guided search and certifying pipeline to compute bounds.
result A four-regime map of tail probabilities with explicit formulas.
We find the exact worst-case tail probability for bounded kurtosis.
problem Determining the worst-case tail probability under bounded kurtosis constraints.
method AI-guided search and certificate verification around the certifying pipeline.
result A four-regime map of tail probabilities with explicit formulas and dual certificates.
The article detects market regimes from covariance matrices using VLSTAR and clustering models.
problem Market regime switching is hard to detect due to time-varying correlation coefficients.
method The article applies VLSTAR and unsupervised hierarchical clustering on monthly realized covariance matrices.
result VLSTAR outperforms clustering in detecting market regimes.
Inference over tails is usually performed by fitting an appropriate limiting distribution over observations that exceed a fixed threshold. However, the choice of such threshold is critical and can affect the inferential results. Extreme value mixture models have been defined to estimate the threshold using the full dat…
This paper analyzes bias-variance trade-off for clipped SFOMs, improving complexity guarantees for heavy-tailed noise.
problem Improving complexity guarantees for stochastic optimization methods with heavy-tailed noise.
method Novel analysis of bias-variance trade-off in gradient clipping for clipped SFOMs.
result Improved complexity guarantees for clipped SFOMs across various tail indices, including infinite mean noise.
New concentration inequalities for tensors with heavy-tailed coefficients.
problem Developing bounds for Euclidean functions of tensors with sub-Weibull distributions.
method Extending concentration inequalities to sub-Weibull random tensors, using new inequalities for heavy-tailed random variables and martingale analysis.
result Established a phase transition between sub-gaussian and heavy-tailed regimes for Euclidean functions of tensors.
Paper proposes a 1-bit quantization scheme for high-dimensional statistical estimation.
problem High-dimensional statistical estimation with limited data.
method Uniformly dithered 1-bit quantization for sparse covariance matrix estimation, sparse linear regression, and matrix completion.
result Near minimax rates in sub-Gaussian regime and improved rates in heavy-tailed regime.
DE-SGD shows heavy-tailed behavior in decentralized settings.
problem Heavy-tailed behavior in decentralized SGD.
method Analyzes the emergence of heavy-tails in DE-SGD, considering both quadratic and twice continuously differentiable strongly convex loss functions.
result DE-SGD exhibits heavier tails than centralized SGD, and tail behavior depends on network parameters.
The study identifies and analyzes different market regimes in equity markets using advanced signal processing techniques.
problem Understanding and quantifying the dynamics of different market regimes in equity markets.
method Data-driven Hilbert--Huang Transform for regime identification, Holo--Hilbert Spectral Analysis for profiling, and Variable-Length Markov Chains for return dynamics modeling.
result Developed markets normalize more effectively as stress subsides, while developing markets retain residual tail dependence and downside persistence.
Paper tackles robust batched bandits for heavy-tailed rewards.
problem Clinical trials and other applications with heavy-tailed rewards.
method Proposes robust batched bandit algorithms for heavy-tailed rewards in finite-arm and Lipschitz-continuous settings.
result Heavier-tailed rewards require fewer batches for near-optimal regret in the instance-independent regime and Lipschitz setting.
Bayesian posterior contraction rates improve with decreasing tails
problem Bayesian posterior contraction in nonparametric settings
method Using p-exponential tails for contraction rates result Improvement in contraction rates with decreasing tails
Large deviations for fat tailed distributions, i.e. those that decay slower than exponential, are not only relatively likely, but they also occur in a rather peculiar way where a finite fraction of the whole sample deviation is concentrated on a single variable. The regime of large deviations is separated from the regi…
Paper presents a dynamic tail risk protection strategy using ML and econometrics.
problem Tail risk protection in finance with solid mathematical and statistical tools.
method Dynamic tail risk protection strategy using weak classifiers (parametric and non-parametric) to estimate exceedance probability and derive trading signals.
result Ensemble classifier improves generalization and trading performance.
Multifractality in time series arises from temporal correlations, not just fat tails.
problem Understanding the origin of multifractality in time series data.
method Mathematical arguments and numerical simulations using MFDFA approach.
result Genuine multifractality requires temporal correlations, not just fat tails.
We propose a stochastic process driven by memory effect with novel distributions including both exponential and leptokurtic heavy-tailed distributions. A class of distribution is analytically derived from the continuum limit of the discrete binary process with the renormalized auto-correlation and the closed form momen…
FinStressTS creates synthetic benchmarks for financial forecasting, revealing model weaknesses.
problem Limited failure attribution in real-world financial benchmarks.
method Synthetic benchmark with 30 diagnostic environments linked to six mechanism families.
result Model performance varies by mechanism type, with autoregressive models often outperforming Transformers.
This paper improves risk control for financial markets by calibrating VaR forecasts using conformal methods.
problem Nonstationary and regime-dependent losses in financial markets.
method Regime-weighted conformal risk control (RWC) for VaR forecasting.
result RWC improves regime-conditional stability in some settings with modest conservativeness changes.
A new tail-shape index based on Value at Risk and Expected Shortfall.
problem Measuring and comparing tail behavior of loss distributions.
method Introducing a new θ-index based on equal level relationships between Value at Risk and Expected Shortfall. result The θ-index provides a level-dependent, scale-free measure of upper tail behavior. We propose a stochastic process driven by the memory effect with novel distributions which include both exponential and leptokurtic heavy-tailed distributions. A class of the distributions is analytically derived from the continuum limit of the discrete binary process with the renormalized auto-correlation. The moment …
Study free energy in spherical spin glasses, proving universality dichotomy.
problem Analyzing free energy in spherical spin glass models with different tail exponents.
method Introduced a tail-adapted normalization and used universality dichotomy.
result Sharp universality dichotomy for free energy across different tail exponents.
This paper presents an empirical investigation of the intraday Brazilian stock market price fluctuations, considering q-Gaussian distributions that emerge from a non-extensive statistical mechanics. Our results show that, when returns are measured over intervals less than one hour, the empirical distributions are well …
Privacy affects how much data is needed for CVaR optimization.
problem Privacy constraints impact the effective sample size for CVaR optimization.
method Analyzes the privacy-relevant sample size and decomposes CVaR excess risk.
result The effective private tail sample size is εnτ, affecting CVaR learning rates.
Local Gaussian correlation struggles in tails but a new method improves it.
problem Local Gaussian correlation's limitations in tail dependence.
method A new adaptive bandwidth method for LGC, optimizing for local effective sample size.
result Adaptive bandwidths outperform global ones in moderate dependence, but not in strong or weak dependence.
Method bounds tail probabilities of continuous RVs.
problem Bounding tail probabilities of continuous random variables.
method Setting continuous, positive, and strictly decreasing/increasing functions to derive upper and lower bounds.
result Provides tighter bounds than existing methods, including a novel asymptotic capacity bound for AWGN channel.
In complex systems such as turbulent flows and financial markets, the dynamics in long and short time-lags, signaled by Gaussian and fat-tailed statistics, respectively, calls for a unified description. To address this issue we analyze a real dataset, namely, price fluctuations, in a wide range of temporal scales to em…
A new method predicts stock ranking uncertainty to improve trading performance during regime shifts.
problem Ranking models fail during regime shifts, leading to suboptimal performance.
method Adapting DEUP to rankers, predicting rank displacement and uncertainty, and proposing a two-level deployment policy.
result The two-level deployment policy improves risk-adjusted performance and indicates DEUP adds value mainly as a tail-risk guard.
Study proposes adaptive RL for dynamic portfolio optimization.
problem Traditional portfolio optimization models fail to adapt to regime shifts.
method Regime-aware reinforcement learning framework with hybrid observations and constrained reward functions.
result Transformer PPO achieves highest risk-adjusted returns, while LSTM variants offer a good balance.
Study characterizes learning from heavy-tailed data in high dimensions using superstatistical methods.
problem Characterizing learning from heavy-tailed data in high-dimensional settings.
method Empirical risk minimization with double-stochastic processes and superstatistical analysis.
result Analytical characterization of separability transition and generalization performance.
Unified framework for generating heavy-tailed distributions.
problem Extending SGMs to heavy-tailed targets.
method Combining early stopping with initialization for diffusion, and normalizing flows for generation.
result Unified generative framework with theoretical guarantees for heavy-tailed distributions.
New method estimates extreme outcomes in heavy-tailed data, breaking circular dependence.
problem Estimating outcomes for extreme events in heavy-tailed data.
method Proposes an ADRF estimator that includes a structured tail-shape output and a diagnostic to evaluate tail shape.
result Successfully reduces MAE in deep-tail and conditional-shortfall predictions.
MARCD uses generative scenarios to improve portfolio decisions during regime shifts.
problem Improving portfolio decisions under regime shifts and drawdowns.
method MARCD employs a Gaussian HMM for regime inference, a diffusion generator for scenario production, and a CVaR allocator with tail-weighted and crisis-aware components.
result MARCD reduces maximum drawdowns by 34% compared to baseline methods over 2020-2025.
Continuous Hidden Markov Models for Equity Returns
problem Generating synthetic equity returns that match real return characteristics
method Continuous Hidden Markov Models
result Recovered volatility clustering and narrowed kurtosis gap
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.
The study examines when large trades are considered news or liquidity shocks in a market model.
problem Understanding when large trades are news or liquidity shocks in a market model.
method A sequential competitive limit order book model with asymmetric information and Student-t tails for liquidity demand.
result Heavy-tailed liquidity demand flattens and concavifies price impact, delaying price discovery.
Sharp large deviations and Gibbs conditioning for portfolio credit risk models.
problem Analyzing the risk of default in financial portfolios with dependent factors.
method Sharp large deviation estimates and conditional Bahadur-Rao estimates for threshold models with diverging latent factors.
result Conditioned on a large exceedance event, default indicators become asymptotically i.i.d., and loss-given-default is exponentially tilted.
RL-CVaR model improves insurance reserving under economic stress.
problem Managing insurance reserve setting under claim development uncertainty and macroeconomic stress.
method Reinforcement Learning (PPO) with CVaR constraints, trained under regime-aware curriculum.
result RL-CVaR policy reduces solvency violations and tail-risk compared to classical methods.
There is convincing evidence showing that the probability distributions of stock returns in mature markets exhibit power-law tails and both the positive and negative tails conform to the inverse cubic law. It supports the possibility that the tail exponents are universal at least for mature markets in the sense that th…
This work analyzes CVaR under heavy-tailed data, providing generalization and robustness bounds.
problem Understanding CVaR's behavior under heavy-tailed data and rare high-impact losses.
method Learning-theoretic analysis of CVaR-based empirical risk minimization.
result Sharp, high-probability generalization and excess risk bounds under minimal moment assumptions.
This study shows ESG ratings reduce equity crash risk during market downturns.
problem Decoupling of alpha from tail risk resilience in traditional models.
method Double Machine Learning for structural deconfounding, state-dependent analysis.
result High ESG ratings reduce crash incidence during systemic drawdowns.