The stationary distribution of a GARCH(1,1) process has a power law decay, under broadly applicable conditions. We study the change in the exponent of the tail decay under temporal aggregation of parameters, with the distribution of innovations held fixed. The parameter transformation we study...

We develop explicit asymptotic expansions of the portfolio Value-at-Risk (VaR) and portfolio Expected Shortfall (ES) for a large family of multivariate elliptical distributions. The family includes distributions of exponential type such as Kotz distributions, and power type such as the...