Related papers: On partial stochastic comparisons based on tail va…
The task for a general and useful classification of the tail behaviors of probability distributions still has no satisfactory solution. Due to lack of information outside the range of the data the tails of the distribution should be…
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…
We generalize Quasi-Linear Means by restricting to the tail of the risk distribution and show that this can be a useful quantity in risk management since it comprises in its general form the Value at Risk, the Tail Value at Risk and the…
In risk management, tail risks are of crucial importance. The assessment of risks should be carried out in accordance with the regulatory authority's requirement at high quantiles. In general, the underlying distribution function is…
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…
We introduce a new class of heavy-tailed distributions for which any weighted average of independent and identically distributed random variables is larger than one such random variable in (usual) stochastic order. We show that many…
Tail dependence refers to clustering of extreme events. In the context of financial risk management, the clustering of high-severity risks has a devastating effect on the well-being of firms and is thus of pivotal importance in risk…
In this paper, we investigate risk measures such as value at risk (VaR) and the conditional tail expectation (CTE) of the extreme (maximum and minimum) and the aggregate (total) of two dependent risks. In finance, insurance and the other…
Tail risk measures are fully determined by the distribution of the underlying loss beyond its quantile at a certain level, with Value-at-Risk, Expected Shortfall and Range Value-at-Risk being prime examples. They are induced by law-based…
In this paper we provide a novel family of stochastic orders that generalizes second order stochastic dominance, which we call the $\alpha,[a,b]$-concave stochastic orders. These stochastic orders are generated by a novel set of "very"…
Extreme values and the tail behavior of probability distributions are essential for quantifying and mitigating risk in complex systems of all kinds. In multivariate settings, accounting for correlations is crucial. Although extreme value…
We consider an investor, whose portfolio consists of a single risky asset and a risk free asset, who wants to maximize his expected utility of the portfolio subject to managing the Value at Risk (VaR) assuming a heavy tailed distribution of…
This paper explores the applications of the 20/60/20 rule-a heuristic method that segments data into top-performing, average-performing, and underperforming groups-in mathematical finance. We review the statistical foundations of this rule…
Designing randomized online algorithms that perform reliably not only in expectation but also under unfavorable realizations of randomness is a fundamental challenge in online decision-making. In this paper, we study this challenge in…
Given a finite collection of stochastic alternatives, we study the problem of sequentially allocating a fixed sampling budget to identify the optimal alternative with a high probability, where the optimal alternative is defined as the one…
While the estimation of risk is an important question in the daily business of banking and insurance, many existing plug-in estimation procedures suffer from an unnecessary bias. This often leads to the underestimation of risk and…
Understanding the shape of a distribution of data is of interest to people in a great variety of fields, as it may affect the types of algorithms used for that data. We study one such problem in the framework of distribution property…
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…
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…
While the {estimation} of risk is an important question in the daily business of banking and insurance, many existing plug-in estimation procedures suffer from an unnecessary bias. This often leads to the underestimation of risk and…