  We present a constructive approach to Bernstein copulas with an admissible
discrete skeleton in arbitrary dimensions when the underlying marginal grid
sizes are smaller than the number of observations. This prevents an overfitting
of the estimated dependence model and reduces the simulation effort for
Bernstein copulas a lot. In a case study, we compare different approaches of
Bernstein and Gaussian copulas w.r.t. the estimation of risk measures in risk
management.
