Related papers: Risk Management with Tail Quasi-Linear Means

An asymptotic model for extreme behavior of certain Markov chains is the "tail chain". Generally taking the form of a multiplicative random walk, it is useful in deriving extremal characteristics such as point process limits. We place this…

This paper proposes a semiparametric joint VaRES framework driven by realized information, mo tivated by the economic mechanisms underlying tail risk generation. Building on the CAViaR quantile recursion, the model introduces a dynamic…

Learning the tail behavior of a distribution is a notoriously difficult problem. By definition, the number of samples from the tail is small, and deep generative models, such as normalizing flows, tend to concentrate on learning the body of…

In this note we prove bounds on the upper and lower probability tails of sums of independent geometric or exponentially distributed random variables. We also prove negative results showing that our established tail bounds are asymptotically…

Motivated by a bidimensional discrete-time risk model in insurance, we study the second-order asymptotics for two kinds of tail probabilities of the stochastic discounted value of aggregate net losses including two business lines. These are…

Economic and financial crises are characterised by unusually large events. These tail events co-move because of linear and/or nonlinear dependencies. We introduce TailCoR, a metric that combines (and disentangles) these linear and…

Recent empirical and theoretical analyses of several commonly used prediction procedures reveal a peculiar risk behavior in high dimensions, referred to as double/multiple descent, in which the asymptotic risk is a non-monotonic function of…

This article introduces a non-parametric information-theoretic approach to inference about the tail of a continuous or a discrete distribution. Leveraging a new concept named tail profile -- a set of information-theoretic quantities…

We look at optimal liability-driven portfolios in a family of fat-tailed and extremal risk measures, especially in the context of pension fund and insurance fixed cashflow liability profiles, but also those arising in derivatives books such…

The inf-convolution of risk measures is directly related to risk sharing and general equilibrium, and it has attracted considerable attention in mathematical finance and insurance problems. However, the theory is restricted to finite sets…

Starting from the requirement that risk measures of financial portfolios should be based on their losses, not their gains, we define the notion of loss-based risk measure and study the properties of this class of risk measures. We…

This paper focuses on a discrete-time risk model in which both insurance risk and financial risk are taken into account. We study the asymptotic behaviour of the ruin probability and the tail probability of the aggregate risk amount.…

We give explicit bounds for the tail probabilities for sums of independent geometric or exponential variables, possibly with different parameters.

We establish new tail estimates for order statistics and for the Euclidean norms of projections of an isotropic log-concave random vector. More generally, we prove tail estimates for the norms of projections of sums of independent…

We investigate the use of optimization to compute bounds for extremal performance measures. This approach takes a non-parametric viewpoint that aims to alleviate the issue of model misspecification possibly encountered by conventional…

We discuss common errors and fallacies when using naive "evidence based" empiricism and point forecasts for fat-tailed variables, as well as the insufficiency of using naive first-order scientific methods for tail risk management. We use…

In this work, we establish risk bounds for the Empirical Risk Minimization (ERM) with both dependent and heavy-tailed data-generating processes. We do so by extending the seminal works of Mendelson [Men15, Men18] on the analysis of ERM with…

This note presents an operational measure of fat-tailedness for univariate probability distributions, in $[0,1]$ where 0 is maximally thin-tailed (Gaussian) and 1 is maximally fat-tailed. Among others,1) it helps assess the sample size…

We consider the problem of simulating loss probabilities and conditional excesses for linear asset portfolios under the t-copula model. Although in the literature on market risk management there are papers proposing efficient variance…

Model risk has a huge impact on any risk measurement procedure and its quantification is therefore a crucial step. In this paper, we introduce three quantitative measures of model risk when choosing a particular reference model within a…