In general, risk of an extreme outcome in financial markets can be expressed as a function of the tail copula of a high-dimensional vector after standardizing marginals. Hence it is of importance to model and estimate tail copulas. Even for moderate dimension, nonparametrically estimating a tail...

Recently there has been an increasing interest in applying elliptical distributions to risk management. Under weak conditions, Hult and Lindskog (2002) showed that a random vector with an elliptical distribution is in the domain of attraction of a multivariate extreme value distribution. In this...

Empirical volatility changes in time and exhibits tails, which are heavier than normal. Moreover, empirical volatility has - sometimes quite substantial - upwards jumps and clusters on high levels. We investigate classical and nonclassical stochastic volatility models with respect to their...

In economics, rank-size regressions provide popular estimators of tail exponents of heavy-tailed distributions. We discuss the properties of this approach when the tail of the distribution is regularly varying rather than strictly Pareto. The estimator then over-estimates the true value in the...

We show that the weak Pareto law, as used to characterize the tail behaviour of income distributions, implies regularly varying tail probabilities, but that the reverse implication does not hold. We also establish implications among other versions of the weak Pareto law.

Suppose are independent subexponential random variables with partial sums. We show that if the pairwise sums of the ’s are subexponential, then is subexponential and . The result is applied to give conditions under which as , where are constants such that is a.s. convergent. Asymptotic tail...

In this article, a special case of two coupled M/G/1-queues is considered, where two servers are exposed to two types of jobs that are distributed among the servers via a random switch. In this model, the asymptotic behavior of the workload buffer exceedance probabilities for the two single...

Power laws in productivity and firm size are well-documented empirical regularities. As they are upper right-tail phenomena, this paper shows that assuming asymptotic power functions for various model primitives (such as demand and firm heterogeneity) are sufficient for matching these...

Using kernel density estimation we find that over their 1990s business cycles the entire distribution of after-tax (disposable) income moved to the right in the United States and Great Britain while inequality declined. In contrast, Germany and Japan experienced less growth, a rise in inequality...

In an urban economy, the distribution of people and real estate prices depends on the location of the central business district of a city. As distance from the city center increases, both prices and population density diminish, for travel costs increase in terms of time and money. As...