arXiv research

Reply to Tetlock et al. on tail risk and probability gap.

New bounds on continuous random variables' right-tail probabilities.

SS-GEN simulates rare events in heavy and light-tailed data.

Econometric framework integrates heavy-tailed distributions with behavioral probability weighting for better asset pricing.

New measures capture tail dependence and non-exchangeability in financial data.

Study on error probability for classification of heavy-tailed renewal processes.

We present a novel procedure for scaling relatively high frequency tail probability and quantile estimates for the conditional distribution of returns.

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

We propose an analytical approach to the computation of tail probabilities of compound distributions whose individual components have heavy tails. Our approach is based on the contour integration method, and gives rise to a representation of the tail probability of a compound distribution in the form of a rapidly conve…

TTF improves performance of normalizing flows for heavy-tailed distributions.

A new tail-shape index based on Value at Risk and Expected Shortfall.

We provide a new extension of Breiman's Theorem on computing tail probabilities of a product of random variables to a multivariate setting. In particular, we give a complete characterization of regular variation on cones in $[0,\infty)^d$ under random linear transformations. This allows us to compute probabilities of a…

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

New method bounds stochastic subgradient methods with heavy-tailed noise.

New algorithms achieve high-probability parameter-free regret in online convex optimization with heavy-tailed data.

Dynamic Vocabulary Pruning stabilizes LLM training by removing low-probability tokens.

We propose a family of models that enable predictive estimation of time-varying extreme event probabilities in heavy-tailed and nonlinearly dependent time series. The models are a white noise process with conditionally log-Laplace stochastic volatility. In contrast to other, similar stochastic volatility formalisms, th…

In the presence of a layer of metaprobabilities (from uncertainty concerning the parameters), the asymptotic tail exponent corresponds to the lowest possible tail exponent regardless of its probability. The problem explains "Black Swan" effects, i.e., why measurements tend to chronically underestimate tail contribution…

The paper proposes a new method to measure risk with fine-grained tail sensitivity.

Method bounds tail probabilities of continuous RVs.

RS-NSGD improves SGD convergence for heavy-tailed noise.

Paper develops a TR-SSQP method for noisy optimization with heavy-tailed noise.

We consider the tail probabilities of stock returns for a general class of stochastic volatility models. In these models, the stochastic differential equation for volatility is autonomous, time-homogeneous and dependent on only a finite number of dimensional parameters. Three bounds on the high-volatility limits of the…

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…

The paper integrates behavioral distortions into portfolio optimization using implied probability weighting functions.

I report a new statistical distribution formulated to confront the infamous, long-standing, computational/modeling challenge presented by highly skewed and/or leptokurtic ("fat- or heavy-tailed") data. The distribution is straightforward, flexible and effective. Even when working with far fewer data points than are rou…

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…

New algorithms improve stopping time for best arm identification.

Paper solves robust convex problems with heavy-tailed noise.

New bounds for heavy-tailed SDEs without info-theory terms.

Paper studies second order tail probabilities in risk models.

Optimal algorithm identifies best arm for risk measures in heavy-tailed distributions.

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

Efficiently estimates sparse mean from heavy-tailed data.

The hidden tail of empirical distributions is analyzed using extreme value theory.

Proposes a new framework to manage venture capital portfolio risk by focusing on deal-level correlations.

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…

TailGAN uses GANs to detect anomalies near data distribution tails.

In this paper a quantitative analysis of the ruin probability in finite time of discrete risk process with proportional reinsurance and investment of finance surplus is focused on. It is assumed that the total loss on a unit interval has a light-tailed distribution -- exponential distribution and a heavy-tailed distrib…

Develops a new divergence framework that combines $f$-divergences and IPMs.

New algorithm finds critical points in non-convex optimization with heavy-tailed gradients.

Financial time series have been investigated to follow fat-tailed distributions. Further, an empirical probability distribution sometimes shows cut-off shapes on its tails. To describe this stylized fact, we incorporate the cut-off effect in superstatistics. Then we confirm that the presented stochastic model is capabl…

Modified lognormal distribution with flexible tails for skewed data.

Exact tail probability bounds for bounded kurtosis.

We find the exact worst-case tail probability for bounded kurtosis.

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

In the world of modern financial theory, portfolio construction has traditionally operated under at least one of two central assumptions: the constraints are derived from a utility function and/or the multivariate probability distribution of the underlying asset returns is fully known. In practice, both the performance…

Optimizes privacy-preserving optimization for heavy-tailed data.