arXiv research

Study on U-statistics with heavy-tailed samples, providing tail bounds and LDP.

New method models fat-tailed distributions with anisotropic tail-adaptive flows.

New ensemble method improves model stability exponentially.

Estimate arrival times in random recursive trees using iterated Jordan centralities.

Study examines implied volatility behavior in Bachelier model.

We prove exponential decay of correlations for Hölder continuous observables with respect to any Gibbs measure for contact Anosov flows admitting Pesin sets with exponentially small tails. This is achieved by establishing strong spectral estimates for certain Ruelle transfer operators for such flows.

Markov chain decoders improve generative models' ability to produce heavy-tailed data.

A random walk $w_n$ on a separable, geodesic hyperbolic metric space $X$ converges to the boundary $\partial X$ with probability one when the step distribution supports two independent loxodromics. In particular, the random walk makes positive linear progress. Progress is known to be linear with exponential decay when …

In this paper we study the asymptotic decay of finite time ruin probabilities for an insurance company that faces heavy-tailed claims, uses predictable investment strategies and makes investments in risky assets whose prices evolve according to quite general semimartingales. We show that the ruin problem corresponds to…

In the Black-Scholes context we consider the probability distribution function (PDF) of financial returns implied by volatility smile and we study the relation between the decay of its tails and the fitting parameters of the smile. We show that, considering a scaling law derived from data, it is possible to get a new f…

The paper examines how heavy-tailed risks behave under Gaussian copula models.

Interpolating models can have heavy-tailed risk, leading to rare but severe errors.

We analyze the slope gap distribution of Veech surfaces, finding finite non-analytic points and quadratic tail decay.

New framework estimates treatment effects in extreme data.

Bayesian inference and superstatistics model financial volatility dynamics across different timescales.

Study optimizes sampling to avoid extreme tail risks in unknown heavy-tailed distributions.

Study examines robust regression in high dimensions with heavy-tailed data.

We obtain sharp bounds on the performance of Empirical Risk Minimization performed in a convex class and with respect to the squared loss, without assuming that class members and the target are bounded functions or have rapidly decaying tails. Rather than resorting to a concentration-based argument, the method used her…

Second part of series studying charged scalar fields on Reissner--Nordström spacetimes.

Efficiently estimates covariance for sub-Weibull vectors with sub-Gaussian rate.

New sampling method for heavy-tailed distributions using Langevin Algorithm.

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…

Conditional Value-at-Risk (CVaR) is a widely used risk metric in applications such as finance. We derive concentration bounds for CVaR estimates, considering separately the cases of light-tailed and heavy-tailed distributions. In the light-tailed case, we use a classical CVaR estimator based on the empirical distributi…

We compare systematically several classes of stochastic volatility models of stock market fluctuations. We show that the long-time return distribution is either Gaussian or develops a power-law tail, while the short-time return distribution has generically a stretched-exponential form, but can assume also an algebraic …

Introduces recency bias to improve time-series forecasting.

Last SGD iterate bounds for overparameterized linear regression.

A self-organized model with social percolation process is proposed to describe the propagations of information for different trading ways across a social system and the automatic formation of various groups within market traders. Based on the market structure of this model, some stylized observations of real market can…

We analyze quantitatively the effect of spurious multifractality induced by the presence of fat-tailed symmetric and asymmetric probability distributions of fluctuations in time series. In the presented approach different kinds of symmetric and asymmetric broad probability distributions of synthetic data are examined s…

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 …

Improved TD learning with tail averaging and regularization achieves optimal convergence rates.

Nonlinear SGD achieves high-probability rates in non-convex optimization with heavy-tailed noise.

Continuous Hidden Markov Models for Equity Returns

This work extends diffusion models to handle heavy-tailed targets, improving score estimation and sampling guarantees.

Ridge regression performs optimally in noisy environments with heavy-tailed distributions.

We found that factors decay over time, with momentum fitting best.

The paper analyzes multivariate Hawkes processes and their induced population processes.

Classic studies of the probability density of price fluctuations $g$ for stocks and foreign exchanges of several highly developed economies have been interpreted using a {\it power-law} probability density function $P(g) \sim g^{-(α+1)}$ with exponent values $α> 2$, which are outside the Lévy-stable regime $0 < α< 2$. …

The quotient of random variables with normal distributions is examined and proven to have have power law decay, with density $f\left( x\right) \simeq f_{0}x^{-2}$, with the coefficient depending on the means and variances of the numerator and denominator and their correlation. We also obtain the conditional probability…

New theory sharpens Q-learning with LDTZ rate, proving it's best of both worlds.

Stability of catenoid in 4D Minkowski space proven without symmetry assumptions.

A hybrid model combines BPH and HE distributions for better heavy-tailed distribution approximation.

Stochastic (sub)gradient methods require step size schedule tuning to perform well in practice. Classical tuning strategies decay the step size polynomially and lead to optimal sublinear rates on (strongly) convex problems. An alternative schedule, popular in nonconvex optimization, is called \emph{geometric step decay…

Improved VAE for heavy-tailed data using Student's t-distributions.

DE-SGD shows heavy-tailed behavior in decentralized settings.

Learning shrinks hard tail, improving inference performance.

The paper studies quantile contributions and their relationship with order statistics in heavy-tailed distributions.

This paper analyzes ETFs with Taiwan exposure, finding heavy tails and asymmetric volatility.

Study shows wealth distribution tails near criticality are not universal.