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Related papers: Implicit max-stable extremal integrals

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We study distributional robustness in the context of Extreme Value Theory (EVT). We provide a data-driven method for estimating extreme quantiles in a manner that is robust against incorrect model assumptions underlying the application of…

Statistics Theory · Mathematics 2020-06-09 Jose Blanchet , Fei He , Karthyek R. A. Murthy

Stochastic gradient descent procedures have gained popularity for parameter estimation from large data sets. However, their statistical properties are not well understood, in theory. And in practice, avoiding numerical instability requires…

Methodology · Statistics 2016-09-29 Panos Toulis , Edoardo M. Airoldi

The Dirichlet forms methods, in order to represent errors and their propagation, are particularly powerful in infinite dimensional problems such as models involving stochastic analysis encountered in finance or physics, cf. [5]. Now, coming…

Probability · Mathematics 2016-11-04 Nicolas Bouleau

For a discrete function $f\left( x\right) $ on a discrete set, the finite difference can be either forward and backward. However, we observe that if $ f\left( x\right) $ is a sum of two functions $f\left( x\right) =f_{1}\left( x\right)…

General Physics · Physics 2021-04-23 Q. H. Liu

We give tight lower and upper bounds on the expected missing mass for distributions over finite and countably infinite spaces. An essential characterization of the extremal distributions is given. We also provide an extension to totally…

Statistics Theory · Mathematics 2011-11-10 Daniel Berend , Aryeh Kontorovich

In this paper, we study a stochastic optimal control problem with stochastic volatility. We prove the sufficient and necessary maximum principle for the proposed problem. Then we apply the results to solve an investment, consumption and…

Portfolio Management · Quantitative Finance 2018-08-15 Rodwell Kufakunesu , Calisto Guambe

Stochastic variational inference makes it possible to approximate posterior distributions induced by large datasets quickly using stochastic optimization. The algorithm relies on the use of fully factorized variational distributions.…

Machine Learning · Computer Science 2014-11-27 Matthew D. Hoffman , David M. Blei

We consider a stochastic volatility model where the moment generating function of the logarithmic price is finite only on part of the real line. Using a new Tauberian result obtained in [1] and [2], we show that the knowledge of the moment…

Pricing of Securities · Quantitative Finance 2016-08-08 Sidi Mohamed Aly

When modeling a vector of risk variables, extreme scenarios are often of special interest. The peaks-over-thresholds method hinges on the notion that, asymptotically, the excesses over a vector of high thresholds follow a multivariate…

Statistics Theory · Mathematics 2024-09-23 Anas Mourahib , Anna Kiriliouk , Johan Segers

We generalize the concept of extremal index of a stationary random sequence to the series scheme of identically distributed random variables with random series sizes tending to infinity in probability. We introduce new extremal indices…

Probability · Mathematics 2020-09-22 Alexey V. Lebedev

The extremal Fourier intensities are studied for stationary Edwards-Wilkinson-type, Gaussian, interfaces with power-law dispersion. We calculate the probability distribution of the maximal intensity and find that, generically, it does not…

Statistical Mechanics · Physics 2013-05-29 G. Gyorgyi , P. C. W. Holdsworth , B. Portelli , Z. Racz

This paper addresses the problem of estimating, in the presence of random censoring as well as competing risks, the extreme value index of the (sub)-distribution function associated to one particular cause, in the heavy-tail case.…

Statistics Theory · Mathematics 2017-01-20 Julien Worms , Rym Worms

For an m-dimensional multivariate extreme value distribution there exist 2^{m}-1 exponent measures which are linked and completely characterise the dependence of the distribution and all of its lower dimensional margins. In this paper we…

Statistics Theory · Mathematics 2012-11-01 Ioannis Papastathopoulos , Jonathan A. Tawn

Rough stochastic volatility models have attracted a lot of attentions recently, in particular for the linear option pricing problem. In this paper, starting with power utilities, we propose to use a martingale distortion representation of…

Mathematical Finance · Quantitative Finance 2017-12-12 Jean-Pierre Fouque , Ruimeng Hu

Let F be a distribution function with negative mean and regularly varying right tail. Under a mild smoothness condition we derive higher order asymptotic expansions for the tail distribution of the maxima of the random walk generated by F.…

Probability · Mathematics 2007-05-23 Ph . Barbe , W. P. McCormick , C. Zhang

We propose a nonparametric estimator of the empirical distribution function (EDF) of the latent spot variance of the log-price of a financial asset. We show that over a fixed time span our realized EDF (or REDF) -- inferred from noisy…

Econometrics · Economics 2026-01-29 Kim Christensen , Martin Thyrsgaard , Bezirgen Veliyev

The aim of this short note is to present a solution to the discrete time exponential utility maximization problem in a case where the underlying asset has a multivariate normal distribution. In addition to the usual setting considered in…

Mathematical Finance · Quantitative Finance 2023-06-27 Yan Dolinsky , Or Zuk

In the framework of Cramer's probabilistic model of primes, we explore the exact and asymptotic distributions of maximal prime gaps. We show that the Gumbel extreme value distribution exp(-exp(-x)) is the limit law for maximal gaps between…

Number Theory · Mathematics 2014-09-30 Alexei Kourbatov

Max-stable processes are a popular tool for the study of environmental extremes, and the extremal skew-$t$ process is a general model that allows for a flexible extremal dependence structure. For inference on max-stable processes with…

Methodology · Statistics 2020-04-21 B. Beranger , A. G. Stephenson , S. A. Sisson

Recently the regular conditional distributions of max-infinitely divisible processes were derived by \citet{Dombry2011} and although these conditional distributions have complicated closed forms, \citet{Dombry2011b} introduce an algorithm…

Statistics Theory · Mathematics 2012-08-28 Clément Dombry , Mathieu Ribatet