In the early 1990s, Avram and Taqqu showed that regularly varying moving average processes with all coefficients nonnegative and the tail index α strictly between 0 and 2 satisfy the functional limit theorem. They also conjectured that an equivalent statement holds under a certain less...

Using regular variation to define heavy tailed distributions, we show that prominent downside risk measures produce similar and consistent ranking of heavy tailed risk. Thus regardless of the particular risk measure being used, assets will be ranked in a similar and consistent manner for heavy...

This paper explores the potential for violations of VaR subadditivity both theoretically and by simulations, and finds that for most practical applications VaR is subadditive. Hence, there is no reason to choose a more complicated risk measure than VaR, solely for reasons of coherence.

It is hard to find explicit expressions for the renewal function U(x)=∑n=0∞F∗n(x). Many researchers have made attempts to find suitable approximations for U(x). In this paper we present simple approximations and show that they cover many of the known results.

We study the first-order bifurcating autoregressive process Xt=ϕX⌊t/2⌋+ϵt with Weibull innovations. Using point process technique, we estimate the model parameter ϕ and the tail index α in the Weibull distribution and obtain the joint limit distribution of estimators.

The tail distortion risk measure at level p∈(0,1) was introduced in  Zhu and Li (2012) and  Yang (2012), where the parameter p represents the confidence level. In this paper, we establish the second-order asymptotics of the risk concentration based on the tail distortion risk measure, as...

This paper characterizes a class of regularly varying production functions with an asymptotic elasticity of substitution equal to one. In particular, it is shown that these functions asymptotically approximate the Cobb–Douglas form. The results generalize and unify existing results in the...

This paper studies the effect of truncation on the large deviations behavior of the partial sum of a triangular array coming from a truncated power law model. Each row of the triangular array consists of i.i.d. random vectors, whose distribution matches a power law on a ball of radius going to...

Relay nodes in an ad hoc network can be modelled as fluid queues, in which the available service capacity is shared by the input and output. In this paper such a relay node is considered; jobs arrive according to a Poisson process and bring along a random amount of work. The total transmission...

The relationship between the theory of elliptically contoured distributions and the concept of tail dependence is investigated. We show that bivariate elliptical distributions possess the so-called tail dependence property if the tail of their generating random variable is regularly varying, and...