Related papers: Diversification for infinite-mean Pareto models wi…

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…

We find the perhaps surprising inequality that the weighted average of independent and identically distributed Pareto random variables with infinite mean is larger than one such random variable in the sense of first-order stochastic…

In this paper, we establish a sufficient condition to compare linear combinations of independent and identically distributed (iid) infinite-mean random variables under usual stochastic order. We introduce a new class of distributions that…

We study the optimal decisions and equilibria of agents who aim to minimize their risks by allocating their positions over extremely heavy-tailed (i.e., infinite-mean) and possibly dependent losses. The loss distributions of our focus are…

Diversification is usually viewed as a reliable way to reduce risk, yet it can dramatically fail for heavy-tailed losses with infinite mean: pooling independent losses of this type may increase tail risk at every threshold. We study this…

In recent years, stochastic dominance for independent and identically distributed (iid) infinite-mean random variables has received considerable attention. The literature has identified several classes of distributions of nonnegative random…

We consider a multivariate heavy-tailed stochastic volatility model and analyze the large-sample behavior of its sample covariance matrix. We study the limiting behavior of its entries in the infinite-variance case and derive results for…

We model the influence of sharing large exogeneous losses to the reinsurance market by a bipartite graph. Using Pareto-tailed claims and multivariate regular variation we obtain asymptotic results for the Value-at-Risk and the Conditional…

Stochastic volatility processes with heavy-tailed innovations are a well-known model for financial time series. In these models, the extremes of the log returns are mainly driven by the extremes of the i.i.d. innovation sequence which leads…

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…

For purposes of Value-at-Risk estimation, we consider several multivariate families of heavy-tailed distributions, which can be seen as multidimensional versions of Paretian stable and Student's t distributions allowing different marginals…

The tail of the distribution of a sum of a random number of independent and identically distributed nonnegative random variables depends on the tails of the number of terms and of the terms themselves. This situation is of interest in the…

Random multiplicative growth with redistribution generates stationary Pareto wealth tails in the Bouchaud-M\'ezard model, but assumes a fixed multiplicative noise intensity. This is restrictive for physical and financial growth processes,…

We obtain concentration and large deviation for the sums of independent and identically distributed random variables with heavy-tailed distributions. Our concentration results are concerned with random variables whose distributions satisfy…

We establish sharp large deviation asymptotics for the maximum order statistic of independent and identically distributed heavy-tailed random variables, valid for all Borel subsets of the right tail. This result yields exact decay rates for…

The most popular approach in extreme value statistics is the modelling of threshold exceedances using the asymptotically motivated generalised Pareto distribution. This approach involves the selection of a high threshold above which the…

Stochastic dominance of a random variable by a convex combination of its independent copies has recently been shown to hold within the relatively narrow class of distributions with concave odds function, and later extended to broader…

We propose a novel probabilistic model to facilitate the learning of multivariate tail dependence of multiple financial assets. Our method allows one to construct from known random vectors, e.g., standard normal, sophisticated joint…

We consider a family of multivariate distributions with heavy-tailed margins and the type I elliptical dependence structure. This class of risks is common in finance, insurance, environmental and biostatistic applications. We obtain the…

Heavy-tailed distributions are infamously difficult to estimate because their moments tend to infinity as the shape of the tail decay increases. Nevertheless, this study shows the utilization of a modified group of moments for estimating a…