Related papers: Corrected phase-type approximations of heavy-taile…

We develop accurate approximations of the delay distribution of the MArP/G/1 queue that cap- ture the exact tail behavior and provide bounded relative errors. Motivated by statistical analysis, we consider the service times as a mixture of…

In many applications, significant correlations between arrivals of load-generating events make the numerical evaluation of the load of a system a challenging problem. Here, we construct very accurate approximations of the workload…

Significant correlations between arrivals of load-generating events make the numerical evaluation of the workload of a system a challenging problem. In this paper, we construct highly accurate approximations of the workload distribution of…

Numerical evaluation of ruin probabilities in the classical risk model is an important problem. If claim sizes are heavy-tailed, then such evaluations are challenging. To overcome this, an attractive way is to approximate the claim sizes…

A perturbative approach is used to derive approximations of arbitrary order to estimate high percentiles of sums of positive independent random variables that exhibit heavy tails. Closed-form expressions for the successive approximations…

Heavy-tailed distributions, prevalent in a lot of real-world applications such as finance, telecommunications, queuing theory, and natural language processing, are challenging to model accurately owing to their slow tail decay. Bernstein…

We consider in this paper a risk reserve process where the claims and gains arrive according to two independent Poisson processes. While the gain sizes are phase-type distributed, we assume instead that the claim sizes are phase-type…

We consider the fitting of heavy tailed data and distribution with a special attention to distributions with a non--standard shape in the "body" of the distribution. To this end we consider a dense class of heavy tailed distributions…

Computation of extreme quantiles and tail-based risk measures using standard Monte Carlo simulation can be inefficient. A method to speed up computations is provided by importance sampling. We show that importance sampling algorithms,…

Considerable literature has been devoted to developing statistical inferential results for risk measures, especially for those that are of the form of L-functionals. However, practical and theoretical considerations have highlighted quite a…

Modern risk modelling approaches deal with vectors of multiple components. The components could be, for example, returns of financial instruments or losses within an insurance portfolio concerning different lines of business. One of the…

A phase-type distribution is the distribution of the time until absorption in a finite state-space time-homogeneous Markov jump process, with one absorbing state and the rest being transient. These distributions are mathematically tractable…

Big data can easily be contaminated by outliers or contain variables with heavy-tailed distributions, which makes many conventional methods inadequate. To address this challenge, we propose the adaptive Huber regression for robust…

The use of expectiles in risk management has recently gathered remarkable momentum due to their excellent axiomatic and probabilistic properties. In particular, the class of elicitable law-invariant coherent risk measures only consists of…

This paper studies the quantization of heavy-tailed data in some fundamental statistical estimation problems, where the underlying distributions have bounded moments of some order. We propose to truncate and properly dither the data prior…

We propose a novel approach for detecting change points in high-dimensional linear regression models. Unlike previous research that relied on strict Gaussian/sub-Gaussian error assumptions and had prior knowledge of change points, we…

Expectiles define the only law-invariant, coherent and elicitable risk measure apart from the expectation. The popularity of expectile-based risk measures is steadily growing and their properties have been studied for independent data, but…

This thesis evaluates most of the extreme mixture models and methods that have appended in the literature and implements them in the context of finance and insurance. The paper also reviews and studies extreme value theory, time series,…

We consider the problem of inference for non-stationary time series with heavy-tailed error distribution. Under a time-varying linear process framework we show that there exists a suitable local approximation by a stationary process with…

Motivated by the prominence of Conditional Value-at-Risk (CVaR) as a measure for tail risk in settings affected by uncertainty, we develop a new formula for approximating CVaR based optimization objectives and their gradients from limited…