We consider the sensitivity of conditional value-at-risk (CVaR) with respect to the tail index assuming regularly varying tails and exponential and faster-than-exponential tail decay for the return distribution. We compare it to the CVaR sensitivity with respect to the scale parameter for stable Paretian, the Student’s t, and generalized Gaussian laws and discuss implications for the modeling o...

We propose a class of weighted least squares estimators for the tail index distribution function with regularly varying tail. Our approach is based on method developed by Holan and McElroy (2010) Parzen index. prove asymptotic normality consistency under suitable assumptions. These earlier are compared in various models through simulation study using mean squared error as criterion. The results...

This paper considers a heterogeneous M / G/2 queue. The service times at server 1 are exponentially distributed, and at server 2 they have a general distribution BO. We present an exact analysis of the queue length and waiting time distribution in case B(·) has a rational Laplace-Stieltjes transform. When B(·) is regularly varying at infinity of index -lI, we determine the tail behaviour of the...

We consider a single-server GI/GI/1 queueing system with feedback. We assume the service times distribution to be (intermediate) regularly varying. We find the tail asymptotics for a customer’s sojourn time in two regimes: the customer arrives in an empty system, and the customer arrives in the system in the stationary regime. In particular, in the case of Poisson input we use the branching pro...

This paper presents a general tail approximation method for evaluating the Valueat-Risk of any norm of random vectors with multivariate regularly varying distributions. The main result is derived using the relation between the intensity measure of multivariate regular variation and tail dependence function of the underlying copula, and in particular extends the tail approximation discussed in E...

High density magnetic domain wall gratings are imprinted in ferromagnetic-antiferromagnetic thin films by local ion irradiation by which alternating head-to-tail-to-head-to-tail and head-to-head-to-tail-to-tail spatially overlapping domain wall networks are formed. Unique magnetic domain processes result from the interaction of anchored domain walls. Non-linear magnetization response is introdu...

A necessary and sufficient condition for the tail of an infinitely divisible distribution on the real line to be estimated by the tail of its Lévy measure is found. The lower limit and the upper limit of the ratio of the right tail μ(r) of an infinitely divisible distribution μ to the right tail ν(r) of its Lévy measure ν as r →∞ are estimated from above and below by reviving Teugels’s classica...

for MA(l) time series J.L. Geluk Liang Peng y Econometric Institute 1 Report EI-9910-A Abstract For samples of random variables with a regularly varying tail estimating the tail index has received much attention recently. For the proof of asymptotic normality of the tail index estimator second order regular variation is needed. In this paper we rst supplement earlier results on convolution give...

The multivariate regular variation (MRV) is one of the most important tools in modeling multivariate heavy-tailed phenomena. This paper characterizes the MRV distributions through the tail dependence function of the copula associated with them. Along with some existing results, our studies indicate that the existence of the lower tail dependence function of the survival copula is necessary and ...

PERT is a widely utilized framework for project management. However, as a result of underlying assumptions about the activity times, the PERT formulas prescribe a light-tailed distribution with a constant variance conditional on the range. Given the pervasiveness of heavy-tailed phenomena in business contexts as well as inherently differing levels of uncertainty about different activities, ther...