English
Related papers

Related papers: Model-free bounds on Value-at-Risk using extreme v…

200 papers

We study variance-dependent regret bounds for Markov decision processes (MDPs). Algorithms with variance-dependent regret guarantees can automatically exploit environments with low variance (e.g., enjoying constant regret on deterministic…

Machine Learning · Computer Science 2023-05-23 Runlong Zhou , Zihan Zhang , Simon S. Du

We consider settings in which the distribution of a multivariate random variable is partly ambiguous. We assume the ambiguity lies on the level of the dependence structure, and that the marginal distributions are known. Furthermore, a…

Mathematical Finance · Quantitative Finance 2020-05-27 Stephan Eckstein , Michael Kupper , Mathias Pohl

For a risk vector $V$, whose components are shared among agents by some random mechanism, we obtain asymptotic lower and upper bounds for the individual agents' exposure risk and the aggregated risk in the market. Risk is measured by…

Risk Management · Quantitative Finance 2016-04-12 Oliver Kley , Claudia Kluppelberg

In classical extreme value theory probabilities of extreme events are estimated assuming all the components of a random vector to be in a domain of attraction of an extreme value distribution. In contrast, the conditional extreme value…

Statistics Theory · Mathematics 2011-08-30 Bikramjit Das , Sidney I. Resnick

We consider the variable selection problem, which seeks to identify important variables influencing a response $Y$ out of many candidate features $X_1, \ldots, X_p$. We wish to do so while offering finite-sample guarantees about the…

Methodology · Statistics 2019-02-12 Rina Foygel Barber , Emmanuel J. Candès , Richard J. Samworth

We derive two related novel bounds on single-variable marginal probability distributions in factor graphs with discrete variables. The first method propagates bounds over a subtree of the factor graph rooted in the variable, and the second…

Probability · Mathematics 2008-01-25 Joris M. Mooij , Hilbert J. Kappen

Let $\mathbf{X}(n) \in \mathbb{R}^d$ be a sequence of random vectors, where $n\in\mathbb{N}$ and $d = d(n)$. Under certain weakly dependence conditions, we prove that the distribution of the maximal component of $\mathbf{X}$ and the…

Probability · Mathematics 2025-04-22 Mikhail Isaev , Igor Rodionov , Rui-Ray Zhang , Maksim Zhukovskii

We present a distribution optimization framework that significantly improves confidence bounds for various risk measures compared to previous methods. Our framework encompasses popular risk measures such as the entropic risk measure,…

Machine Learning · Computer Science 2023-06-13 Hao Liang , Zhi-quan Luo

We consider the problem of risk diversification of $\alpha$-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…

Risk Management · Quantitative Finance 2017-04-25 Umberto Cherubini , Paolo Neri

Given finite-dimensional random vectors $Y$, $X$, and $Z$ that form a Markov chain in that order (i.e., $Y \to X \to Z$), we derive upper bounds on the excess minimum risk using generalized information divergence measures. Here, $Y$ is a…

Information Theory · Computer Science 2025-06-02 Ananya Omanwar , Fady Alajaji , Tamás Linder

This paper extends standard results from learning theory with independent data to sequences of dependent data. Contrary to most of the literature, we do not rely on mixing arguments or sequential measures of complexity and derive uniform…

Machine Learning · Computer Science 2023-03-22 Fabien Lauer

In this paper we study a model-based approach to calculating approximately optimal policies in Markovian Decision Processes. In particular, we derive novel bounds on the loss of using a policy derived from a factored linear model, a class…

Machine Learning · Statistics 2016-09-22 Bernardo Ávila Pires , Csaba Szepesvári

A general class of models is proposed that is able to estimate the whole predictive distribution of a dependent variable $Y$ given a vector of explanatory variables $\xb$. The models exploit that the strength of explanatory variables to…

Methodology · Statistics 2021-03-25 Gerhard Tutz

This paper studies multivariate Value-at-Risk (VaR) for financial portfolios with a focus on modeling dependence structures through Archimedean copulas. Using the generator representation of Archimedean copulas, we derive explicit…

Methodology · Statistics 2026-02-03 Dotamana Yéo , Saralees Nadarajah , Amadou Sawadogo

In this paper, we explore bounds on the expected risk when using deep neural networks for supervised classification from an information theoretic perspective. Firstly, we introduce model risk and fitting error, which are derived from…

Machine Learning · Computer Science 2024-10-08 Binchuan Qi

Consider the problem of drawing random variates $(X_1,\ldots,X_n)$ from a distribution where the marginal of each $X_i$ is specified, as well as the correlation between every pair $X_i$ and $X_j$. For given marginals, the…

Probability · Mathematics 2016-12-30 Mark Huber , Nevena Maric

The aim of this paper is to provide several novel upper bounds on the excess risk with a primal focus on classification problems. We suggest two approaches and the obtained bounds are represented via the distribution dependent local…

Statistics Theory · Mathematics 2018-03-13 Nikita Zhivotovskiy

This brief paper summarize the chances offered by the Peak-Over-Threshold method, related with analysis of extremes. Identification of appropriate Value at Risk can be solved by fitting data with a Generalized Pareto Distribution. Also an…

Applications · Statistics 2015-09-04 Gianluca Rosso

We prove lower bounds on the error of any estimator for the mean of a real probability distribution under the knowledge that the distribution belongs to a given set. We apply these lower bounds both to parametric and nonparametric…

Statistics Theory · Mathematics 2024-03-05 Rémy Degenne , Timothée Mathieu

We study off-policy reinforcement learning for controlling continuous-time Markov diffusion processes with discrete-time observations and actions. We consider model-free algorithms with function approximation that learn value and advantage…

Machine Learning · Computer Science 2026-04-17 Wenlong Mou