  We consider the problem of simulating loss probabilities and conditional
excesses for linear asset portfolios under the t-copula model. Although in the
literature on market risk management there are papers proposing efficient
variance reduction methods for Monte Carlo simulation of portfolio market risk,
there is no paper discussing combining the randomized quasi-Monte Carlo method
with variance reduction techniques. In this paper, we combine the randomized
quasi-Monte Carlo method with importance sampling and stratified importance
sampling. Numerical results for realistic portfolio examples suggest that
replacing pseudorandom numbers (Monte Carlo) with quasi-random sequences
(quasi-Monte Carlo) in the simulations increases the robustness of the
estimates once we reduce the effective dimension and the non-smoothness of the
integrands.
