We characterize convergence of a sequence of d-dimensional random vectors by convergence of the one-dimensional margins and of the copula. The result is applied to the approximation of portofolio modelled by t-copulas with large degrees of freedom, and to the convergence of certain dependence...

Lévy processes and infinitely divisible distributions are increasingly defined in terms of their Lévy measure. In order to describe the dependence structure of a multivariate Lévy measure, Tankov (2003) introduced Lévy copulas on <formula format="inline"><file name="sjos_527_mu1.gif" type="gif" /></formula>. (For an extension to <b><openface>R</openface>-super-<b>""m""</b></b>, see Kallsen & Tankov,...

Extreme value theory for a class of EGARCH processes is developed. It is shown that the EGARCH process as well as the logarithm of its conditional variance lie in the domain of attraction of the Gumbel distribution. Norming constants are obtained and it is shown that the considered processes...

Central limit theorem, quadratic variation, bipower variation

Central limit theorem, quadratic variation, bipower variation

Using positive semidefinite supOU (superposition of Ornstein-Uhlenbeck type) processes to describe the volatility, we introduce a multivariate stochastic volatility model for financial data which is capable of modelling long range dependence effects. The finiteness of moments and the second...

Expressions for (absolute) moments of generalized hyperbolic and normal inverse Gaussian (NIG) laws are given in terms of moments of the corresponding symmetric laws. For the (absolute) moments centred at the location parameter "μ" explicit expressions as series containing Bessel functions are...