Bayesian method improves extreme quantile estimation with zero coverage error.
problem Estimating extreme quantiles with zero coverage error in small samples.
method Bayesian quantile estimation using Jeffreys prior.
result Bayesian method results in zero coverage error, unlike maximum likelihood.
For purposes of Value-at-Risk estimation, we consider several multivariate families of heavy-tailed distributions, which can be seen as multidimensional versions of Paretian stable and Student's t distributions allowing different marginals to have different tail thickness. After a discussion of relevant estimation and …
This paper analyzes the equilibrium distribution of wealth in an economy where firms' productivities are subject to idiosyncratic shocks, returns on factors are determined in competitive markets, dynasties have linear consumption functions and government imposes taxes on capital and labour incomes and equally redistrib…
We introduce a stochastic model to explain a double power-law distribution which exhibits two different Paretian behaviors in the upper and the lower tail and widely exists in social and economic systems. The model incorporates fitness consideration and noise fluctuation. We find that if the number of variables (e.g. t…
We consider a generalization of the Heath Jarrow Morton model for the term structure of interest rates where the forward rate is driven by Paretian fluctuations. We derive a generalization of Itô's lemma for the calculation of a differential of a Paretian stochastic variable and use it to derive a Stochastic Differenti…
We propose a network description of large market investments, where both stocks and shareholders are represented as vertices connected by weighted links corresponding to shareholdings. In this framework, the in-degree (kin) and the sum of incoming link weights (v) of an investor correspond to the number of asset…
Pareto distributions, and power laws in general, have demonstrated to be very useful models to describe very different phenomena, from physics to finance. In recent years, the econophysical literature has proposed a large amount of papers and models justifying the presence of power laws in economic data. Most of the ti…
We study the distribution P(ω) of the random variable ω= x_1/(x_1 + x_2), where x_1 and x_2 are the wealths of two individuals selected at random from the same tempered Paretian ensemble characterized by the distribution Ψ(x) \sim φ(x)/x^{1 + α}, where α> 0 is the Pareto index and φ(x) is the cut-off function. We con…
New method models fat-tailed distributions with anisotropic tail-adaptive flows.
problem Gaussian-based variational inference fails to accurately capture tail decay in fat-tailed distributions.
method Improved theory on tails of flows, developed anisotropic tail-adaptive flows (ATAF).
result ATAF models tail-anisotropy, outperforming prior work on synthetic and real-world targets.
New measures capture tail dependence and non-exchangeability in financial data.
problem Underestimation of tail dependence and inability to capture non-exchangeable tail dependence.
method Tail copulas and novel tail dependence measures (MTCM, ATCM) are proposed.
result Captures non-exchangeable tail dependence and provides analytical forms for various copulas.
The paper examines how heavy-tailed risks behave under Gaussian copula models.
problem Understanding tail risk probabilities with heavy-tailed marginal risks and Gaussian dependence.
method Modeling heavy-tailed risks using regular variation and analyzing tail probabilities under Gaussian copula.
result The rate of decay of tail set probabilities varies with the type of tail sets and Gaussian correlation matrix.
New tail dependence measures for stock indices.
problem Measuring tail dependence between financial variables.
method Introducing a new stochastic order and studying monotone tail dependence measures.
result Advantage of new tail dependence measures over classical ones.
Study tail behavior of sum of heavy-tailed risks with copulas.
problem Analyzing the tail behavior of sums of heavy-tailed risks with dependence modeled by copulas.
method Modeling dependence with copulas and analyzing tail asymptotics of sums of heavy-tailed risks.
result Obtained asymptotic expansions for Value-at-Risk of aggregate risk.
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.
A simple log-transform fixes heavy-tailed data for generative models.
problem Standard generative models struggle with heavy-tailed data.
method Apply the soft-log transform to data before training and exponentiate samples after generation.
result Log-FM outperforms specialized baselines on multivariate benchmarks.
SS-GEN simulates rare events in heavy and light-tailed data.
problem Estimating probabilities of extreme events in multivariate data.
method Self-Similar Generative Estimation (SS-GEN) decomposes tail distribution into radial and angular components.
result SS-GEN generates representative extreme scenarios and estimates rare-event probabilities beyond observed data.
This work extends diffusion models to handle heavy-tailed targets, improving score estimation and sampling guarantees.
problem Score estimation and sampling guarantees for heavy-tailed targets in diffusion models.
method Kernel density estimation and minimax rates analysis for score estimation and sampling guarantees.
result Sharp minimax rates for score estimation and sampling guarantees for heavy-tailed targets, revealing qualitative differences between exponential and polynomial tails.
The literature of heavy tails (typically) starts with a random walk and finds mechanisms that lead to fat tails under aggregation. We follow the inverse route and show how starting with fat tails we get to thin-tails when deriving the probability distribution of the response to a random variable. We introduce a general…
This paper improves tail dependence analysis by introducing a path-based approach.
problem The classical tail dependence coefficient fails to capture non-exchangeable features of tail dependence.
method The paper introduces a path-based maximal tail dependence approach to capture the most pronounced feature of dependence over all possible paths.
result The paper proves the existence and provides an explicit characterization of the path-based maximal TDC, improving analytical and computational tractability.
HTFM improves mode coverage and tail-statistic recovery for heavy-tailed data.
problem Tackles heavy-tailed data in various domains with rare events.
method Proposes a framework using clock-conditioned Gaussian sources and truncated logsignature features.
result Improves mode coverage, sample quality, and tail-statistic recovery over Gaussian flow matching and baselines.
The paper explores tail diversification in financial markets using entropy and mutual information.
problem Tail diversification in financial time series.
method Statistical independence through differential entropy and mutual information, using moments as contrast functions.
result Tail covariance matrix is a key driver of tail diversification.
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.
Study on U-statistics with heavy-tailed samples, providing tail bounds and LDP.
problem Deviation of U-statistics with heavy-tailed samples.
method Exponential tail bounds and Large Deviation Principle (LDP) for U-statistics.
result Obtained an exponential upper bound for U-statistics tail decay, showing two regions of decay.
TTF improves performance of normalizing flows for heavy-tailed distributions.
problem Improving performance of normalizing flows for heavy-tailed distributions.
method Uses a Gaussian base distribution and a final transformation layer to produce heavy tails.
result Experimental results show TTF outperforms current methods, especially in high-dimensional or heavy-tailed scenarios.
New method allocates capital based on tail central moments for financial risk assessment.
problem Inability of CTE-based capital allocation to reflect tail behavior of losses.
method Developed TCM-based capital allocation for normal mean-variance mixture distributions.
result TCM-based method captures tail risk contributions not detected by CTE.
PH-VAE models heavy-tailed data with flexible Phase-Type distributions.
problem Standard VAEs fail to capture heavy-tailed behavior in real-world data.
method PH-VAE uses Phase-Type distributions defined by continuous-time Markov chains to adaptively model tail behavior.
result PH-VAE significantly outperforms existing heavy-tail-aware VAEs in approximating diverse heavy-tailed distributions.
Heavy-tailed distributions emerge in SGD's parameter evolution.
problem Understanding heavy-tailed distributions in SGD parameter evolution.
method Continuous diffusion approximation of SGD (homogenized SGD) analysis.
result Explicit upper and lower bounds on tail-index of homogenized SGD.
This paper measures and compares the tail risks of limit and market orders using Extreme Value Theory. The analysis examines realised tail outcomes using the Dealing 2000-2 electronic broking system based on completed transactions rather than the more common analysis of indicative quotes. In general, limit and market o…
COMET Flows model multivariate extremes with heavy tails and asymmetric dependence.
problem Normalizing flows struggle with multivariate extremes and asymmetric tail dependence.
method COMET Flows decomposes modeling into marginal and copula parts; uses tail belief and kernel density for marginals, and low-dimensional manifold for tail dependence.
result COMET Flows outperform other models in capturing heavy-tailed marginals and asymmetric tail dependence.
C. Armond, S. Garoufalidis and T.Le have shown that a unicolored Jones polynomial of a B-adequate link has a stable tail at large colors. We categorify this tail by showing that Khovanov homology of a unicolored link also has a stable tail, whose graded Euler characteristic coincides with the tail of the Jones polynomi…
Paper introduces MTCM to measure multivariate tail dependence.
problem Classical TDC fails to capture non-exchangeable features of multivariate tail dependence.
method Extends bivariate tail copula measure to multivariate case.
result MTCM reveals off-diagonal stress directions and differences in extremal dependence.
Paper improves ETF tail-risk monitoring reliability.
problem Unreliable ETF risk monitoring under degraded data.
method Combines quality checks, prediction, scoring, and adjustment.
result Improves tail-risk monitoring, especially during stressed periods.
The book chapter discusses tail risk analysis for financial data using extreme value statistics.
problem Serial dependence in financial time series complicates tail risk assessment.
method The approach involves unconditional and conditional quantile forecasting.
result Serial dependence impacts multivariate tail dependence.
The paper assesses how equity tail risk impacts US Treasury bond returns.
problem The effects of equity tail risk on the US government bond market.
method Estimating equity tail risk using option-implied stock market volatility and assessing its predictive power in reduced-form regressions and a term structure model.
result Equity tail risk significantly predicts one-month excess returns on Treasuries.
New framework controls generalization for heavy-tailed data in RLHF and SGLD.
problem Heavy-tailed data in modern learning pipelines.
method Tail-dependent information-theoretic framework for sub-Weibull data.
result Sharp generalization bounds for heavy-tailed data.
We consider the problem of risk diversification of α-stable heavy tailed risks. We study the behaviour of the aggregated Value-at-Risk, with particular reference to the impact of different tail dependence structures on the limits to diversification. We confirm the large evidence of sub-additivity violations, particul…
A new algebra for probabilistic programming improves tail behavior accuracy.
problem Inaccurate tail behavior in probabilistic models based on neural networks.
method Developed a three-parameter tail asymptotics algebra based on the generalized Gamma distribution.
result Inference algorithms using the heavy-tailed algebra achieve superior performance.
Paper improves normalizing flows to better capture distribution tails.
problem Difficult to learn tail behavior of distributions.
method Develops a new type of flows using flexible base distributions and data-driven linear layers.
result Improves accuracy, especially on distribution tails, and generates heavy-tailed data.
Novel framework for reliable long-tailed classification.
problem Challenges of long-tailed imbalance and specific error risks.
method Bayesian Decision Theory and variational optimization.
result Demonstrates reliability and flexibility in diverse tasks.
New insights into tail behavior of heavy-tailed random vectors and processes.
problem Understanding tail behavior of aggregates of heavy-tailed random vectors.
method Analyzing multivariate regularly varying random vectors and Lévy processes.
result More than one large jump can determine tail behavior of aggregates.
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.
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.
Study on heavy tails in closing auction returns, explaining imbalance through limit order submission.
problem Understanding heavy tails in closing auction return distributions.
method Used the stochastic call auction model of Derksen et al. (2020a) to derive and verify a relation between tail exponents.
result Large closing price fluctuations are not caused by large market orders, but by imbalance in limit orders.
Self-regulating annealing improves sampling from heavy-tailed datasets.
problem Sampling from heavy-tailed distributions using diffusion models.
method Proposed an SDE-based sampler with a state-dependent diffusion coefficient.
result State dependence induces a self-regulating annealing mechanism.
A new method improves posterior approximation for complex distributions.
problem Difficulty in capturing multimodal and heavy-tailed posteriors with standard normalizing flows.
method StiCTAF: stick-breaking mixture base with component-wise tail adaptation.
result Improved tail recovery and better mode coverage compared to benchmarks.
Reply to Tetlock et al. on tail risk and probability gap.
problem Expert judgment fails to account for tail risk.
method Comparison of forecasting tournaments and extreme value theory.
result Greater gap between tail expectation and probability properties.
The tail of the distribution of a sum of a random number of independent and identically distributed nonnegative random variables depends on the tails of the number of terms and of the terms themselves. This situation is of interest in the collective risk model, where the total claim size in a portfolio is the sum of a …
New method optimizes tail dependence coefficient estimation.
problem Estimating tail dependence in nonparametric data.
method Optimal threshold selection combining mean squared error and copula estimation.
result Improved accuracy in tail dependence coefficient estimation.