Financial institutions rely heavily on Value-at-Risk (VaR) as a risk measure, even though it is not globally subadditive. First, we theoretically show that the VaR portfolio measure is subadditive in the relevant tail region if asset returns are multivariate regularly varying, thus allowing for...

We propose a semi-parametric method for unconditional Value-at-Risk (VaR) evaluation. The largest risks are modelled parametrically, while smaller risks are captured by the non-parametric empirical distribution function. A comparison of methods on a portfolio of stock and option returns reveals...

We describe all possibilities for sample path properties of H-self-similar [alpha]-stable processes with stationary increments for all pairs ([alpha], H), completing the picture presented by Kôno and Maejima (1991).

This paper studies the sample path properties of stochastic processes represented by multiple symmetric [alpha]-stable integrals. It relates the "smoothness" of the sample paths to the "smoothness" of the (non-random) integrand. It also contains results about the behavior of the distribution of...

Let X1, X2,..., Xn be jointly [alpha]-stable random variables, 0 < [alpha] < 2, and let p1, p2,..., pn be non-negative numbers. We give a necessary and sufficient condition for E X1 p1 ... Xn pn to be finite.

A system with heavy tailed service requirements under heavy load having a single server has an equilibrium waiting time distribution which is approximated by the Mittag-Leffler distribution. This fact is understood by a direct analysis of the weak convergence of a sequence of negative drift...

Some theoretical and practical aspects antithetic and common random numbers for variance reduction in simulation of stochastic systems with dependent elements are considered. A proof of their optimality in estimating the expected value of the response sum or the response difference of a pair of...